John  Swett 


•«  Cambriirge  Courst  of 


ELEMENTS 


OF 


ASTRONOMY 


BY 


W.    J.    ROLFE    AND    J.    A.    GILLET, 

TEACHERS  IN  THE  HIGH   SCHOOL,   CAMBRIDGE,    MASS. 


SECOND    EDITION, 

REVISED  AND   ENLARGED. 


BOSTON: 
CROSBY    AND    AINSWORTH. 

NEW   YORK:    O.   S.   FELT. 
1868. 


•  <      I 

.'    .     .  . 


QB4-3 

P  L& 


Entered  according  to  Act  of  Congress,  in  the  year  1868,  by 

W.  J.   ROLFE  AND  J.   A.   GILLET, 
in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


fij^  O  Cw  •>.  J "  <  JiNi 
EDUCATION  DEPT, 


UKIVERSITY  PRESS  :  WELCH,  BIGELOW,  &  Ca, 
CAMBRIDGE. 


PREFACE 

TO  THE  SECOND   EDITION. 

THE  method  of  treatment  in  this  ASTRONOMY  agrees 
with  that  adopted  in  other  parts  of  the  Course,  so  far  as 
the  nature  of  the  subject  will  admit.  The  aim  throughout 
has  been  to  show  the  scholar  from  what  facts  of  observa- 
tion, and  by  what  processes  of  reasoning,  astronomers 
have  reached  their  present  knowledge  of  the  structure  of 
the  universe. 

The  authors  believe  that  the  principles  which  lie  at  the 
bottom  of  the  explanation  of  most  astronomical  phenom- 
ena are  really  simple,  and,  if  rightly  presented,  capable 
of  being  understood  by  high-school  scholars  of  ordinary 
ability.  They  do  not  assume,  however,  that  the  explana- 
tions given  in  this  book  are  in  all  cases  full  enough  to 
enable  the  teacher  to  dispense  with  oral  instruction. 

The  first  part  of  the  book  treats  of  the  motions  and  dis- 
tances of  the  heavenly  bodies ;  the  second,  of  their  physi- 
cal features ;  and  the  third,  of  gravity,  or  the  force  by 
which  they  act  upon  one  another.  In  this  edition  a  fourth 
part,  treating  of  the  origin,  transmutation,  and  conserva- 
tion of  energy,  has  been  added,  since  it  forms  a  fitting 
conclusion  to  the  Astronomy,  and  also  to  the  whole 
Course. 

In  no  portion  of  the  book  is  there  assumed,  on  the  part 
of  the  pupil,  any  knowledge  of  mathematics  beyond  that 
of  the  elements  of  plane  geometry,  and  an  ability  to  prove 
that  in  plane  triangles  the  sines  of  the  angles  are  propor- 

541830 


iv  PREFACE. 

tional  to  their  opposite  sides.  That  it  may  not  be  neces- 
sary for  scholars  to  study  trigonometry  before  taking  up 
this  book,  this  last  proposition  is  .demonstrated  in  an 
Appendix. 

In  the  Appendix,  the  principal  constellations  have  been 
described,  and  illustrated  by  seventeen  star-maps.  These 
maps  have  been  reduced  by  photography  from  the  excel- 
lent charts  in  Argelander's  Uranometria  Nova.  In  order, 
however,  that  the  maps  in  this  reduced  form  might  not  be 
too  crowded,  all  stars  below  the  fourth  magnitude  have 
been  omitted,  as  well  as  the  circles  of  right  ascension  and 
declination.  The  dotted  lines  have  been  added  by  the 
authors  to  assist  in  tracing  the  leading  stars  in  each  con- 
stellation. 

The  Appendix  also  contains  an  outline  of  the  history 
and  mythology  of  the  constellations  ;  an  account  of  the 
metric  system  and  the  calendar  ;  and  various  astronomical 
tables, 

In  the  preparation  of  the  first  and  third  parts  of  this 
book  the  authors  have  made  free  use  of  Airy's  "  Popular 
Astronomy"  (London,  1866).  In  many  instances  material 
has  been  taken  from  this  source  with  little  alteration,  ex- 
cept that  it  has  been  condensed  and  the  language  sim- 
plified. Yet  the  method  of  treatment  which  we  have  em- 
ployed is  quite  different  from  that  adopted  by  Airy. 

The  material  of  the  second  part  of  the  volume  has  been 
drawn  largely  from  the  English  translation  of  Guille- 
min's  "  Heavens  "  (London,  1866),  Hind's  "  Solar  System  " 
(London,  1851),  and  Hind's  "Astronomy"  (London,  1863.) 

The  division  of  labor  in  preparing  the  book  has  been 
the  same  as  was  explained  in  the  Preface  to  Part  First. 

CAMBRIDGE,  March  5,  1868. 


TABLE   OF   CONTENTS. 


PAGE 
MOTIONS   AND    DISTANCES    OF  THE    HEAVENLY 

BODIES i 

THE  SHAPE  OF  THE  HEAVENLY  BODIES        ...  3 

THE  APPARENT  MOTIONS  OF  THE  STARS  ....  5 

THE  APPARENT  MOTIONS  OF  THE  SUN         .•  •    .        .  21 

TWILIGHT     .•'      .•       .•       .•       .•-      .        ...        .  29 

THE  APPARENT  MOTION  OF  THE  MOON       .        .       .  32 

THE  APPARENT  MOTIONS  OF  THE  PLANETS      ...  34 

THE  PTOLEMAIC  SYSTEM       ;.    "  ..       .    •    '..       .  •     .  35 

THE  SYSTEM  OF  TYCHO  DE  BRAKE   .        .        .     •'••,    -    .  38 

THE  COPERNICAN  SYSTEM      .       . '      .       .       . .     .  39 

THE  SYSTEM  OF  KEPLER    ,)>      .        .'      .       .       .        .  40 

SUMMARY.        .'       .       .'  ..:. .       .       .       .    '   .       .  42 

HOW  TO  FIND  THE  PERIODIC  TIMES  OF  THE  PLANETS   .  45 

SUMMARY.        .'      .        .       ."•".'       .        .        i   "    .  48 
HOW  TO  FIND  THE  DISTANCE  OF  THE  PLANETS  FROM 

THE  SUN  .        .        .  -,   :.        .        .        .        .        .        .  49 

SUMMARY         •   .    ,•        •        •     .........       .  66 

HOW  TO  FIND  THE  DISTANCE  OF  THE  MOON  ...  67 

SUMMARY         .'.'.. 74 

A  GENERAL  SURVEY  OF  THE  ORBITS  OF  THE  PLANETS  .  75 

HOW  TO   FIND  THE    DISTANCE  OF  THE   FlXED   STARS  76 

SUMMARY    U-:'»     '. .     '  .     '- *    '  •.      • .       v.    .-       .  88 

SYSTEMS  OF  SATELLITES  AND  SUNS       .       .       ...  89 

SUMMARY  '.  ,     '  .  .  '  ..    '',.     "  .        ,        *       .        .        .  96 

PHYSICAL  FEATURES  OF  THE  HEAVENLY  BODIES  97 

THE  SUN  '    .        .    *   .    '    .  •  ~  .    "    «-.      ;    •    . .  '•' »        .  99 

THE  NATURE  OF  SUN-SPOTS   .     ',  .        .       .        ».       ..  113 

SUMMARY     .    '  .    '.  ,:  '  »       .  •  .'  . "  '  .     '  .-      ...       .  118 

MERCURY      '  .     '  .        .       .       .     '  ,       ....  120 

VENUS  .     '  .     '  .    "  ,;    "  .    '  .     '  \  '     ..        .        .       .  124 

THE  ZODIACAL  LIGHT      .    '    .    "    .      :i'   '  .'       .        .  127 


VI  TABLE  OF  CONTEXTS. 

THE  EA*TH  .       »....••       ...    09 

THE  MOON       .....  .       .       .        129 

BUUMJ&     ......      -  ..    .       .       .142 

SODCAKT  or  THE  Moon  AKD  Jfimnu  *  .  152 


'57 

OF  THE  INNE*  GROCP  OF  PLANETS  .  .  160 

MDKML  PLANETS 161 

OF  THE  MINOT  PLANETS 166 

JUPTTE* 167 

IT* 

t -  -  i?S 

ITS 

OF  THE  Ovm  GEOCP  OF  PLANETS  .  .  i  So 

181 

1*4 

THE  Frrm  STAIS 185 

SUMMARY 197 

GRAVITY.  OR  THE  FORCE  BY  WHICH  THE  HEAV- 
ENLY   BODIES    ACT    UPON    ONE    ANOTHER  199 

THE  LAWS  OF  MOTION 201 

THE  PENDCLUM      ........  210 

SnOCAKY  OF  THE  PEXDCT.UM 215 

GRAVITY  ACTS  aajmij^x  THE  EAETH  AND  THE  Mooar  216 
GEATTTY  ACTS  BETWEES  THE  SUN  AND  PLANETS,  AXD 

^^••••L  PLANETS  AND  THEZE  MOONS      .        .        .  21$ 

GlATITY  ACTS  «!Ll»lJm  THE  SUN   AND  COMTTS       .  .  225 

GULYTTY  ACTS  AMDNG  AH.  THE   HEAVENLY  BODIES     .  226 


GXATTTY  ACTS   UPON   THE   PAKTICI-ES  OF  \LATTEX  .  257 

SnOLUtT        ..........  ^ 

HOW  TO  FIND  THE  WEIGHT  OF  THE   HEAVENLY  BODIES  247 

SrXXATT        ..........  3^1 

GENTXJLL  SnotAiY  ........  262 


ORIGIN,  TRANSMUTATION,  AND  CONSERYATION 

OF  ENERGY  .........  271 

SnotAiY         .       .......       .  299 

AWESDLX       ..........  301 

aaaauoL       ........  307 


METUC  SYSTEM  .       .       .       .       .       .       .       .512 

ASTMKOMJCAL  TAMLES  .....   -  .       .       jxS 


CAMJI    M 


APPENDIX 
THE 

CoacsnuuiTioxs  TISBLE  EACH  MOCTH       .  331 

STAXS  or  THE  Futsr  MACXFTUBC     .  332 

THE  HMBUM  or  THE  CossrELunoffs      .      .  .       332 

THE  MTTHOLOGT  or  IBB  C0«nu4XMMi    «       .  .    334 

QugiMiM*  PBK.  ggjnnr  ASP  FYUfmanag        -  -       343 

INDEX       ...........    335 


I. 

MOTIONS  AND   DISTANCES   OF 
THE   HEAVENLY  BODIES. 


MOTIONS  AND  DISTANCES  OF  THE 
HEAVENLY   BODIES. 


1.  AT  the  beginning  of  our  study  of  Physics  we  came  to 
the  conclusion  that  matter  is  made  up  of  insensible  masses 
called  molecules,  and  that  these  molecules  are  separated  by 
spaces,  which,  though  probably  thousands  of  times  greater 
than  their  own  bulk,  are  yet  insensibly  small.     We  have 
also  learned  that  many,  and  probably  all,  of  these  mole- 
cules are  made  up  of  yet  smaller  parts,  called  atoms. 

Hitherto  we  have  been  mainly  occupied  with  the  con- 
sideration of  the  forces  which  act  upon  these  atoms  and 
molecules  through  insensible  distances. 

We  now  pass  to  the  study  of  the  earth  and  the  heavenly 
bodies,  and  the  forces  which  act  upon  them  through  the 
spaces  by  which  they  are  separated. 

THE    SHAPE    OF    THE    HEAVENLY    BODIES. 

2.  The  Shape  of  the  Earth.  —  For    several    thousand 
years  men  supposed  that  the  earth  was  »a  large  platform, 
and  that,  if  one  went  far  enough,  he  would  everywhere 
come  to  the  edge,  as  one  does  at  the  sea-shore.     As  soon, 
however,  as  they  began  to  make  long  voyages  at  sea,  it 
was  seen  that  the  sea  is  not  flat,  but  rounded  like  a  low 
hill ;  for  wherever  we  go  at  sea,  we  always  see  the  masts 
of  ships  a  long  way  off  before  we  can  see  the  hull  or  body 
of  the  ship,  though,  so  far  as  size  goes,  the  latter  would  be 


' 4  ,   -  , ."  ASTRONOMY. 

much  easier  to  be  seen.  The  sea  cuts  off  the  view  just 
like  a  hill  rising  between  the  two  ships.  It  was  also  found 
that  the  distance  at  which  ships  of  the  same  height  begin 
to  be  seen  is  everywhere  the  same,  and  as  light  is  known 
to  come  in  straight  lines,  the  hill  of  sea  between  the  two 
ships  must  be  everywhere  the  same.  This  can  be  so  only 
on  a  globe,  that  is,  on  a  body  whose  surface  is  rounded 
equally  in  every  direction. 

We  see,  then,  that  the  surface  of  the  ocean  is  spherical, 
and  when  we  remember  that  about  three  fourths  of  the 
surface  of  the  earth  is  covered  with  water,  it  seems  prob- 
able that  the  whole  surface  of  the  earth  is  spherical. 

Again,  in  an  eclipse  of  the  moon,  we  always  see  a 
shadow  with  a  round  edge  moving  across  its  disc.  This 
shadow  has  never  any  other  shape,  whether  the  eclipse  be 
great  or  small,  and  whatever  part  of  the  earth  be  facing 
the  moon  at  the  time.  Now  this  shadow  is  known  to  be 
the  shadow  of  the  earth,  and  a  body  which  casts  a  round 
shadow  in  every  position  must  be  a  sphere. 

The  earth,  therefore,  must  be  a  globe,  or  sphere. 

3.  The  Sun,  Moon,  and  Planets  are  Globes,  —  The  disc 
of  the  sun  is  always  circular.  The  same  is  true  of  that 
of  the  moon,  though  at  times  we  see  only  a  part  of  its  disc. 
The  same  is  true  of  all  the  planets,  which  bodies  always 
present  sensible  discs  when  viewed  with  the  telescope. 
Now  it  is  well  known  that  these  bodies  do  not  always 
present  the  same  side  to  the  earth ;  and,  as  a  sphere  is 
the  only  body  that  presents  a  circular  outline  from  what- 
ever position  it  is  looked  at,  we  see  that  the  sun,  moon, 
and  planets  are  also  globes. 

The  fixed  stars  present  no  sensible  disc  when  viewed 
with  the  most  powerful  telescope,  therefore  we  know  noth- 
ing about  the  shape  of  these  bodies. 


ASTRONOMY. 


THE    APPARENT    MOTIONS    OF    THE    STARS. 

4.  If,  on  a  clear  night,  we  watch  the  eastern  horizon 
through  its  whole  extent  from  north  to  south,  we  see  stars 
continually  rising;  and  if  we  watch  the  western  horizon 
through  its  whole  extent  from  north  to  south,  we  see 
stars  continually  setting.  We  see,  also,  that  the  stars  do 
not  rise  perpendicularly,  but  obliquely.  Those  which  rise 
near  to  the  north  or  near  to  the  south  rise  very  slantingly 
indeed.  Those  nearest  to  the  east  rise  less  obliquely. 
The  same  is  true  of  their  setting.  Those  near  to  the 
north  or  to  the  south  set  very  obliquely ;  those  which  set 
nearest  to  the  west  set  with  a  sharp  incline.  If  we  trace 
the  whole  path  of  any  one  of  these  stars,  we  find  that  it 
rises  somewhere  in  the  east  in  the  sloping  direction  al- 
ready described ;  that  it  continues  to  rise  with  a  path 
becoming  more  and  more  horizontal,  till  it  reaches  a  cer- 
tain height  in  the  south,  when  its  course  is  exactly  hori- 
zontal ;  and  that  it  then  declines  by  similar  degrees,  and 
sets  at  a  place  in  the  west  just  as  far  from  the  north  point 
as  the  place  where  it  rose  in  the  east. 

If  we  select  a  star  that  has  risen  near  to  the  north,  it 
takes  it  a  long  time  to  rise  to  its  greatest  height,  which 
is  very  high  in  the  south,  and  then  an  equally  long  time 
to  set.  Lastly,  if  we  look  to  the  north  and  observe 
those  stars  which  are  fairly  above  the  horizon,  we  find 
them  going  around  the  Polar  Star  and  describing  a  com- 
plete circle.  These  stars  are  called  circumpolar. 

The  Polar  Star  to  an  ordinary  observer  does  not  appear 
to  change  its  place  during  the  whole  night.  Whenever  he 
looks  out,  he  finds  it  in  the  same  place.  Careful  observa- 
tion, however,  shows  that  it  does  change  its  place  and 
moves  in  a  small  circle.  The  stars  'of  the  Great  Bear  and 
of  Cassiopeia  turn  in  a  circle  considerably  larger  than  the 
i* 


6  ASTRONOMY. 

Polar  Star,  but  they  go  completely  round  in  it  without 
descending  below  the  horizon.  Capella  and  Vega  de- 
scribe still  longer  circles,  of  which  the  Pole  Star  is  the 
centre.  These  stars  pass  below  the  horizon  in  the  north, 
and  pass  nearly  overhead  when  farthest  to  the  south. 

Thus,  if  we  fix  a  straight  rod  in  a  certain  standard  direc- 
tion, pointing  nearly,  but  not  exactly,  to  the  Polar  Star,  we 
find  that  the  stars  which  are  close  in  the  direction  of  this 
rod,  as  seen  by  viewing  along  it,  describe  a  very  small  cir- 
cle ;  the  stars  farther  from  it  describe  a  larger  circle ;  oth- 
ers just  touch  the  northern  horizon  ;  whilst,  in  regard  to 
others,  if  they  do  describe  a  whole  circle  at  all,  part  of  that 
circle  is  below  the  horizon ;  they  are  seen  to  come  up  in 
the  east,  to  pass  the  south,  and  to  go  down  in  the1  west, 
and  they  are  lost  below  the  horizon  from  that  place  till 
they  rise  again  in  the  east. 

5.  Are  the  Movements  of  the  Stars  such  that  they  appear 
to  describe  accurate  Circles  about  a  Point  of  the  Sky  near  the 
Polar  Star  as  a  Centre  ?  —  To  answer  this  question  we  must 
use  an  instrument  called  the  Equatorial.  One  form  of  this 
instrument  is  represented  in  Figure  i.  It  turns  round  an 
axis  A  J3,  which  is  placed  in  the  direction  which  leads 
to  the  point  of  the  sky  around  which  the  stars  appear  to 
turn,  and  which  is  not  far  from  the  Polar  Star.  This  axis 
carries  the  telescope  CD.  As  the  instrument  turns  on 
its  axis  the  telescope  retains  the  same  inclination  to  this 
axis  unless  another  motion  is  given  it  at  the  same  time. 
The  telescope  is,  however,  so  arranged  that  another  mo- 
tion may  be  given  to  it,  so  as  to  place  it  in  different  posi- 
tions, as  C'  D\  C"D" .  It  can  thus  be  directed  to  stars  in 
different  parts  of  the  heavens.  If  now  the  telescope  is 
directed  to  any  one  star,  it  is  found,  by  turning  the  instru- 
ment on  its  axis,  that  the  telescope,  without  any  alteration 
of  its  inclination  to  the  axis,  will  follow  that  star  from  its 
rising  to  its  setting.  It  is  the  same  wherever  the  star  may 


ASTRONOMY. 


Fig.  2. 


be,  whether  near  the  Polar  Star  or  far  from  it.  The  tel- 
escope will  follow  the  star  by  merely  turning  the  instru- 
ment on  its  axis. 

The  movement  of  the  stars,  then,  is  of  such  a  kind  that 
they  appear  to  describe  accurate  circles  about  a  point  of 
the  sky  near  the  Pole  Star  as  a  centre ;  for  it  is  evident 
that  the  telescope,  when  the  instrument  is  turned  on  its 
axis,  describes  such  a  circle,  and,  as  seen,  the  telescope 
always  points  to  the  star  to  which  it  was  directed. 

6.  The  Stars  move  at  a  uniform  Rate,  and  all  describe  their 
Circles  in  the  same  Time.  —  The  best  equatorials  are  fur- 
nished with  a  toothed  wheel  attached  to  the  axis,  in  which 
works  an  endless  screw  or  worm,  as  seen  in  Figure  i. 
By  turning  this  worm  the  whole  instrument  is  made  to 
revolve.  The  worm  is  turned  by  an  apparatus  constructed 
especially  for  producing  uniform  movement.  The  one 
usually  adopted,  with  some  modification,  is  represented 
in  Figure  2.  The  lower  drum  is  turned  by  a  falling 
weight,  and  its  motion  is  regulated  by  the  centrifugal  balls 
A  B,  similar  to  those  which  are  used  to  regulate  the  mo- 


8  ASTRONOMY. 

tion  of  a  steam-engine.  It  is  well  known  that  whirling 
the  balls,  by  the  rotation  of  the  axis  to  which  they  are 
attached,  causes  them  to  spread  out,  and  the  more  rapidly 
they  are  whirled  the  more  they  spread. 

When  the  speed  has  reached  a  certain  limit,  the  spread- 
ing out  of  the  balls  causes  their  arms  to  rub  against  the 
fixed  part,  S  H.  This  friction  prevents  further  accelera- 
tion, and  thus  a  uniform  speed  is  produced  with  very  great 
nicety.  The  spindle  KL  from  this  apparatus  is  attached 
to  the  screw  which  carries  the  equatorial.  It  causes  the 
telescope  of  the  equatorial  to  revolve  around  its  axis  uni- 
formly, and  thus  gives  us  the  means  of  ascertaining  with 
the  utmost  exactness  whether  or  not  the  stars  move  with 
uniform  speed.  When  the  machinery  is  in  operation  the 
telescope  is  pointed  to  a  star.  Whether  this  star  be  near 
the  pole  or  at  a  distance  from  the  pole,  it  is  found  that  it 
is  constantly  seen  in  the  field  of  view  of  the  telescope ; 
that  is,  the  telescope  turns  just  as  fast  as  the  star  moves. 
Now  as  the  telescope  is  moving  with  a  uniform  speed,  it 
follows  that  all  the  stars  are  describing  their  orbits  in  the 
same  time,  and  that  each  star  moves  with  the  same  speed 
in  every  part  of  its  orbit.  The  stars  then  move  as  though 
they  were  attached  to  a  shell,  which  rotates  at  a  uniform 
rate  from  east  to  west  about  an  axis  passing  from  a  point 
of  the  sky  near  the  Polar  Star  through  the  centre  of  the 
earth.  This  axis  is  therefore  called  the  celestial  axis,  and 
the  point  of  the  sky  near  the  Polar  Star  is  called  the  north 
celestial  pole. 

7.  Refraction.  —  When  a  telescope  of  considerable  power 
is  attached  to  the  equatorial,  so  that  we  can  see  a  small 
departure  from  the  centre  of  the  telescope  in  the  position 
of  the  star  we  are  looking  at,  and  when  we  trace  the 
course  of  the  star  down  to  the  horizon,  we  find  it  to  be  a 
universal  fact  that  the  star  is  not  quite  so  near  the  horizon 
as  we  should  be  led  to  expect.  This  is  due  to  refraction. 


ASTRONOMY. 


We  have  already  learned  that  a  ray  of  light  in  passing 
from  a  rarer  into  a  denser  medium  is  always  bent  toward 
a  perpendicular  to  the  surface  of  this  medium.  The  earth 
is  surrounded  by  an  atmosphere,  and  we  will  suppose,  at 
first,  that  this  atmosphere  has  a  definite  boundary  and  a 
uniform  density.  Let  Figure  3  represent  a  part  of  the  earth 
covered  by  the  atmosphere.  Suppose  a  beam  of  light  is 
coming  from  a  star  in  the  direction  A  B,  and  that  it  meets 
the  atmosphere  at  B.  In  passing  into  this  denser  medi- 
um it  is  bent  toward  a  line 
perpendicular  to  the  sur- 
face of  the  atmosphere, 
and  takes  the  direction 
B  C.  Consequently  the 
star  would  be  seen  in 
the  direction  CB.  This 
would  be  the  case  if  the 
atmosphere  had  a  defi- 
nite boundary  and  a  uni- 
form density.  But  if  the  atmosphere  has  not  a  definite 
boundary  and  varies  in  density  from  stratum  to  stratum, 
becoming  more  and  more  dense  as  we  near  the  earth,  the 
ray  of  light  would  be  bent  as  described  above  in  passing 
from  one  stratum  to  the  next.  This  condition  of  things 
is  shown  in  Figure  4.  The  star  would  be  seen  in  the 
position  f,  instead  of  its  real  position  A.  The  effect  of 
refraction  is,  then,  to  cause 
all  the  stars  to  appear  nearer 
the  zenith  (the  point  directly 
overhead)  than  they  really 
are.  If  a  star  were  exactly 
in  the  zenith,  its  position 
would  not  be  changed  by 
refraction,  since  the  ray  of 
light  coming  from  the  star 


IO  ASTRONOMY. 

would  meet  each  stratum  of  air  perpendicularly.  The  far- 
ther a  star  is  from  the  zenith,  the  more  is  it  displaced  by 
refraction,  since  the  light  coming  from  it  would  meet  each 
stratum  more  obliquely,  and  the  more  obliquely  the  ray  of 
light  meets  the  surface  of  the  denser  medium,  the  more  is 
its  direction  bent. 

8.  Does  the  Celestial  Sphere  really  rotate  about  the  Earth 
from  East  to  West?  —  It  was  for  a  long  time  supposed 
that  the  starry  heavens  turned  round  the  earth  daily,  and 
that  the  apparent  motion  of  the  stars  was  real.  But  when 
it  was  discovered  that  the  earth  is  round,  it  was  at  once 
seen  that  the  visible  motion  of  the  heavenly  bodies  could 
be  explained  as  well  by  supposing  that  the  earth  rotates 
from  west  to  east  about  an  axis  which  has  the  same  direc- 
tion as  the  axis  about  which  the  celestial  sphere  appears 
to  rotate  from  east  to  west,  as  by  supposing  that  this 
sphere  does  really  rotate.  The  supposition  that  the  earth 
rotates  instead  of  the  heavens  is  the  simpler  of  the  two, 
and  the  fact  that  the  earth  does  thus  rotate  is  capable  of 
the  following  direct  proof.  It  is  found  that  when  a  heavy 
ball  is  suspended  by  a  long  and  flexible  string,  at  the 
equator,  and  made  to  vibrate,  its  vibrations  appear  to  take 
place  always  in  the  same  direction ;  that  is,  if  it  is  set  vi- 
brating in  a  north  and  south  direction,  it  will  continue  to 
vibrate  in  that  direction;  while  if  a  ball  similarly  sus- 
pended is  set  to  vibrating  anywhere  north  of  the  equator, 
the  direction  in  which  it  vibrates  appears  to  be  continually 
changing.  Now  we  know  that  a  body  when  once  put  in 
motion  tends  always  to  move  in  the  same  absolute  direc- 
tion, and  it  is  reasonable  to  suppose  that  the  heavy  ball, 
when  once  set  swinging,  will  always  vibrate  in  the  same 
absolute  direction,  provided  that  nothing  interferes  with 
its  motion.  If  the  point  from  which  the  ball  is  suspended 
is  twirled  while  the  ball  is  swinging,  its  direction  of  vibra- 
tion does  not  change  ;  and  if  the  point  is  moved  forward 


ASTRONOMY.  1 1 

in  a  straight  line,  or  in  the  circumference  of  a  circle,  its 
directions  of  vibration  are  always  parallel  to  one  another. 
Suppose  now  that  the  earth  be  rotating  from  west  to  east, 
and  that  a  ball  be  suspended  at  the  equator ;  the  motion 
of  the  earth  would  carry  the  point  of  suspension  around  in 
a  circle,  and  the  same  would  be  true  were  the  ball  sus- 
pended north  of  the  equator.  Suppose  now  that  a  ball 
at  the  equator,  and  one  some  way  north  of  the  equator, 
were  both  set  swinging  in  a  north  and  south  direction; 
what  would  be  the  apparent  direction  of  the  vibration  of 
the  ball  in  each  case,  on  the  supposition  that  the  earth 
rotates  ?  In  each  case,  as  we  have  seen,  the  vibrations  of 
the  ball  would  be  parallel  to  one  another.  On  the  sup- 
position that  the  earth  rotates  on  its  axis  from  west  to  east, 
are  the  directions  which  at  different  times  we  call  north 
and  south  parallel  to  one  another,  or  not  ?  We  must  first 
see  what  we  mean  by  north  and  south. 

Suppose  that  two  straight  rods  are  fastened  to  a  terres- 
trial globe,  one  at  the  equator  and  the  other  some  way 
north  of  the  equator,  close  by  the  brass  meridian  and  par- 
allel to  it.  These  rods,  of  course,  would  point  north  and 
south  to  observers  at  these  two  points  on  the  globe.  Now 
rotate  the  globe,  and  the  rod  fastened  at  the  equator  is 
seen  to  remain  parallel  to  the  brass  meridian,  while  the 
rod  north  of  the  equator  begins  to  deviate  at  once  from  a 
direction  parallel  to  the  meridian,  and  deviates  more  and 
more  till  the  globe  has  rotated  through  90°,  when  it  be- 
gins again  to  approach  this  direction,  and  when  the  globe 
has  rotated  through  180°  it  is  again  parallel  to  the  brass 
meridian.  At  the  equator,  then,  on  the  supposition  that 
the  earth  is  rotating,  the  directions  which  an  observer  at 
a  given  place  would  at  different  times  call  north  and  south 
are  parallel  with  one  another;  while  at  a  place  north  or 
south  of  the  equator  the  directions  which  an  observer  at 
different  times  calls  north  and  south  are  continually  chan- 
ging, although  they  appear  to  be  always  the  same. 


1 2  ASTRONOMY. 

If,  then,  the  vibrations  of  the  ball  suspended  as  described 
above  are  always  in  the  same  absolute  direction,  and  the 
ball  be  set  swinging  from  north  to  south,  its  vibrations  at 
the  equator  ought  to  appear  to  be  always  in  the  same  di- 
rection •  while  at  a  point  north  of  the  equator  its  plane  of 
vibration  ought  to  appear  continually  shifting  in  a  direc- 
tion contrary  to  that  in  which  the  north  and  south  direc- 
tion is  really  shifting.  This  is  just  what  is  found  to  be 
true  on  trial.  The  experiment  was  first  made  by  Foucault 
at  Paris  in  1851,  and  has  been  often  repeated  with  the 
same  results.  It  was  tried  in  this  country  some  years 
ago,  in  the  Bunker  Hill  Monument. 

The  supposition,  then,  that  the  earth  rotates  on  its  axis 
from  west  to  east  must  be  true,  and  the  starry  heavens 
are  really  at  rest.  That  the  earth  appears  to  be  at  rest 
and  the  heavens  rotating,  is  not  surprising  when  we  re- 
member that,  on  looking  out  at  the  window  of  a  railway 
car  while  the  train  is  in  rapid  motion,  we  seem  to  be  at 
rest,  and  the  fences  and  trees  to  be  shooting  past  us  in  the 
opposite  direction. 

9.  The  Direction  of  the  Circles  described  by  the  Apparent 
Motion  of  the  Stars  is  different  in  different  Parts  of  the  Earth. 
—  The  circles  described  by  the  stars  in  their  apparent 
daily  motion  are  always  perpendicular  to  the  axis  of  the 
earth.  In  our  latitude  they  are  oblique  to  the  horizon, 
sloping  from  the  south.  They  are  oblique  to  the  horizon 
because  the  horizon  here  is  inclined  to  the  earth's  axis.* 
At  the  equator  the  horizon  is  parallel  to  this  axis,  and 
the  circles  described  by  the  stars  are  consequently  per- 
pendicular to  the  horizon.  South  of  the  equator  the  hori- 
zon is  inclined  to  the  axis  in  a  direction  opposite  to  that 
in  which  it  is  inclined  north  of  the  equator,  and  the  circles 
described  by  the  stars  are  again  oblique  to  the  horizon, 
but  sloping  from  the  north.  At  the  poles  the  horizon  is 
perpendicular  to  the  earth's  axis,  and  the  circles  described 
*  See  Appendix,  II. 


ASTRONOMY. 


Fig. 


by  the  stars  are  consequently  parallel  to  the  horizon. 
Those  stars  which  are  nearer  to  the  elevated  pole  than 
the  horizon  is,  are  always  in  view;  while  those  nearer 
the  depressed  pole  than  the  horizon  is,  are  always  out  of 
sight.  At  any  point  north  of  the  equator,  the  north  pole 
of  the  heavens  is  elevated  above  the  horizon,  and  the  south 
pole  depressed  below  it.  Hence  north  of  the  equator  the 
north  pole  is  the  elevated  pole,  and  the  south  pole  the 
depressed  pole.  South  of  the  equator,  of  course,  it  is 
just  the  reverse. 

10.  The  Fixed  Stars  appear  in  the  same  Position  in  the 
Sky,  from  whatever  Part  of  the  Earth  they  are  observed.  — 
It  is  necessary  to  find  some  way  of  describing  the  position 
of  a  star,  as  seen  in  the  sky,  in  order  to  ascertain  whether  it 
is  seen  in  the  same  position  from  different  parts  of  the  earth. 

I  wish  to  describe  the  position  of  a  speck,  D  (see  Fig- 
ure 5),  on  a  wall,  so  that  any 
person  could  mark  the  posi- 
tion of  the  speck  on  a  similar 
wall  elsewhere.     I  could  de- 
scribe   the    position    of   the 
speck  by  giving  the  horizon- 
tal distance,  A   C,  from  one 
end  of  the  wall,  and  the  ver- 
tical distance,  CD,  from  the  floor,  or  by  giving  the  meas- 
ure of  the  distance  A  D  from  the  corner  A,  and  of  the 
distance  E  D  from  the  corner  E.     I  might  also  give  the 
measure  of  the  distance  A  C,  and  of  the  inclination  of 
the  line  A  D  to  the  horizon. 

It  is  thus  seen  that  there  are  several  ways  of  describing 
the  position  of  the  speck,  but  that  in  every  case  two  meas- 
ures are  necessary.  The  two  measures  which  are  neces- 
sary for  defining  the  position  of  any  point  on  a  surface  are 
called  the  co-ordinates  of  the  point.  Thus  the  distances 
A  C  and  CD  are  co-ordinates  of  the  point  D.  So  also  the 

2 


14  ASTRONOMY. 

distances  A  D  and  E  Z>,  and  the  distance  A  C  and  the 
angle  D  A  C  are  co-ordinates  of  the  point  D. 

Suppose  we  wish  to  define  the  position  of  a  point  on  a 
celestial  globe.  We  could  do  it  most  conveniently  by 
giving  its  distance  from  the  pole  of  the  globe  measured  in 
degrees,  and  the  distance  that  the  globe  must  rotate  from 
a  certain  point  before  this  point  comes  under  the  brass 
meridian.  These  two  distances,  both  measured  in  degrees, 
would  be  the  co-ordinates  of  the  point. 

Suppose,  for  instance,  there  is  a  fixed  point  marked  on 
every  celestial  globe,  and  I  wish  to  tell  some  one  at  a  dis- 
tance the  position  of  a  second  mark,  which  I  have  found 
on  my  globe.  I  find  that  I  must  rotate  the  globe  23°  to 
the  westward  from  the  fixed  point  to  bring  the  mark  under 
the  brass  meridian,  and  that  the  mark  is  36°  from  the  north 
pole  of  the  globe.  I  send  these  co-ordinates  to  the  dis- 
tant person,  and  he  sets  his  globe  so  that  the  fixed  point 
is  under  the  brass  meridian,  and  rotates  it  23°  westward. 
He  now  knows  that  the  point  is  under  the  meridian.  He 
next  measures  along  the  meridian  36°  from  the  given  pole, 
and  he  knows  the  exact  position  of  the  point.  If  the 
globe  were  stationary  and  the  brass  meridian  movable,  we 
could  describe  the  position  of  the  point  equally  well  by 
giving  its  angular  distance  from  one  of  the  poles  of  the 
globe,  and  the  angular  distance  through  which  the  meridian 
must  be  turned  from  a  fixed  point,  in  order  to  bring  the 
point  under  it. 

If  now  we  suppose  an  imaginary  arc  of  a  great  circle 
passing  directly  over  our  heads  and  through  the  celestial 
poles,  and  fixed  to  the  earth  in  such  a  manner  as  to  be 
carried  around  with  it  in  its  rotation  from  west  to  east, 
we  can  evidently  describe  the  position  of  a  star  in  the 
sky  by  ascertaining  how  far  this  imaginary  meridian  must 
sweep  from  a  fixed  point  to  bring  the  star  under  it,  and 
by  ascertaining  its  angular  distance  from  one  of  the  celes- 


ASTRONOMY.  15 

tial  poles  when  under  this  meridian.  The  angular  distance 
of  a  star  from  a  celestial  pole,  and  the  angular  distance  that 
an  imaginary  meridian  must  sweep  over  from  a  fixed  point 
in  order  to  bring  the  star  under  it,  are  the  most  convenient 
co-ordinates  of  a  star. 

ii.  The  Measurement  of  the,  Angular  Distance  that  the 
Meridian  must  sweep  over  in  order  to  bring  the  Star  under  it. 
—  The  measurement  of  the  angular  space  over  which  the 
meridian  must  sweep  from  a  fixed  point  to  bring  the  star 
under  it  is  effected  by  means  of  a  Transit  Instrument. 
This  instrument  is-  represented  in  Figure  6.  It  consists 


Fig.  6. 


of  a  telescope  mounted  on  an  axis,  A  JB,  in  such  a  way 
that  when  it  turns  around  on  this  axis  the  line  C  D  E 
prolonged  to  the  sky  will  describe  the  imaginary  meridian 


1 6  ASTRONOMY. 

just  spoken  of.  This  curve  must  be  perpendicular  to  the 
horizon,  must  divide  the  visible  heavens  into  two  equal 
parts,  and  must  pass  through  the  poles  of  the  heavens. 

To  meet  the  first  condition,  it  is  necessary  that  the  axis 
A  B  be  exactly  horizontal.  To  meet  the  second  condi- 
tion, it  is  necessary  that  the  telescope  CD  be  exactly 
square  with  its  axis  A  B.  The  astronomer  ascertains 
whether  the  telescope  be  exactly  square  with  its  axis  or 
not,  by  looking  at  a  distant  mark,  first,  with  the  pivots 
A  and  B  of  the  instrument  resting  on  the  piers  a  and  £, 
and  then  with  the  axis  turned  over  so  that  the  pivots  A 
and  B  rest  on  the  piers  b  and  a.  If  the  telescope  points 
equally  well  to  the  mark  in  both  positions  of  the  axis,  it 
is  exactly  square  with  its  axis. 

The  astronomer  ascertains  whether  the  instrument  is  so 
adjusted  that  the  curve  described  by  the  line  C  D  E  pro- 
longed shall  pass  through  the  celestial  pole,  by  means  of 
the  Polar  Star.  This  star,  as  has  already  been  stated, 
describes  a  small  circle  about  the  celestial  pole  as  a 
centre.  Let  FGHIKL  represent  this  circle.  Sup- 
pose that  in  turning  the  transit  instrument  about  its  axis, 
the  line  CDE  prolonged,  traces  the  line  G I  or  FK,  as 
the  case  may  be.  The  Polar  Star  in  its  revolution  passes 
that  line  twice ;  and  if  the  line  passes  through  the  celes- 
tial pole,  which  is  the  centre  of  the  circle,  the  arcs  FHK 
and  KL  F  must  be  equal,  and  as  the  motion  of  the  star 
is  uniform,  it  will  take  it  just  as  long  to  pass  from  F  to  Ky 
as  from  K  to  F.  If  these  arcs  are  described  in  equal 
times,  the  instrument  is  properly  adjusted. 

By  means  of  the  transit  instrument  objects  can  be 
viewed  only  when  they  come  under  the  meridian.  Some 
bright  star,  as  Altair,  is  selected,  and  the  time  when  it 
comes  under  the  meridian  accurately  observed  by  means 
of  the  transit  instrument  and  the  clock.  The  time  when 
it  next  comes  under  the  meridian  is  also  carefully  ob- 


ASTRONOMY.  1 7 

served,  and  the  interval  between  these  two  transits  of  the 
star  across  the  meridian  is  called  a  sidereal  day.  This 
day  is  divided  into  twenty-four  equal  parts  called  sidereal 
hours.  The  clock  used  in  the  observatory  is  called  a 
sidereal  clock,  and  is  so  constructed  that  it  would  de- 
scribe just  twenty^four  hours  between  two  successive  tran- 
sits of  the  same  star,  if  its  movements  were  perfectly 
accurate.  In  practice  it  is  found  impossible  to  construct 
a  perfectly  accurate  clock.  The  rate  at  whicrr  the  clock 
gains  or  loses  time  is  ascertained  by  observing  the  suc- 
cessive transits  of  the  same  star,  and,  this  being  known, 
it  becomes  easy  to  reduce  every  observation  to  true  si- 
dereal time.  The  sidereal  clock  should  beat  seconds,  and 
the  beats  should  be  very  distinctly  given. 

To  facilitate  the  determination  of  the  exact  time  when  a 
star  or  planet  comes  under  the  meridian,  a  number  of  cob- 
web threads  are  strung  across  the  focus  of  the  telescope 
at  equal  distances,  parallel  to  one  another  and  to  the  mo- 
tion of  the  telescope  as  it  is  turned  on  its  axis.  These  are 
called  cross-wires.  The  observer  notices  a  star  approaching 
the  meridian.  He  directs  the  telescope  so  as  to  observe 
the  star  when  it  actually  crosses  the  meridian,  and  looks 
into  the  telescope.  Just  before  the  star  begins  to  cross 
the  wires,  he  looks  at  the  face  of  the  clock  for  the  hours 
and  minutes;  he  then  listens  to  the  beats  of  the  clock, 
and  thus  finds  the  hour,  minute,  second,  and  fraction  of  a 
second  when  the  star  crosses  each  wire ;  then,  by  taking 
the  mean  of  these  times,  he  finds  the  time  at  which  the 
star  passes  the  meridian.  The  same  observations  are  made 
with  star  after  star,  as  they  approach  the  meridian,  and 
when  these  observations  have  been  corrected  for  the 
error  of  the  clock,  the  interval  of  time  which  elapses  be- 
tween the  transit  of  a  given  star  and  the  other  stars  ob- 
served becomes  known.  And  as  the  apparent  rotation  of 
the  celestial  sphere  is  uniform,  we  thus  find  one  of  the 

2* 


i8 


ASTRONOMY. 


co-ordinates  by  which  the  position  of  a  star  is  defined, 
—  that  is,  the  distance  that  the  imaginary  meridian  must 
turn  from  a  given  point  in  order  to  bring  the  star  under 
it.  Suppose  the  bright  star  Vega  to  be  taken  as  the 
starting-point,  and  suppose  we  find  that  a  given  star  is 
under  the  meridian  two  hours  afterward.  The  meridian 
must  then  turn  through  30°  from  Vega  in  order  to  bring 
the  star  under  it. 

12.  The  Mural  Circle.  —  The  next  thing  is  to  ascertain 
the  angular  distance  of  the  star  from  the  pole  of  the 
heavens  when  it  is  under  the  meridian.  This  is  ascer- 
tained by  means  of  the  Mural  Circle.  One  form  of  this 

Fig.  7. 


instrument  is  represented  in  Figure  7.  A  is  a  stone  pier 
which  supports  the  axis  of  the  instrument,  and  to  which 
microscopes,  a,  b,  c,  d,  e,  and  /  are  attached.  The  face 
of  the  pier  which  carries  the  microscopes  fronts  either 
the  east  or  the  west.  The  axis  carries  the  circle  B  C 


ASTRONOMY.  19 

and  the  telescope  F  G.  The  telescope  is  fastened  to  the 
circle,  so  that  both  must  move  together.  This  circle  is 
graduated  on  its  outside  into  degrees,  minutes,  and  other 
subdivisions.  The  microscopes  serve  as  pointers  for  ob- 
serving the  exact  position  of  the  circle,  and  by  their  aid 
the  space  between  the  divisions  can  be  subdivided  with 
great  exactness. 

We  wish  to  know  in  any  observation  how  far  the  tele- 
scope points  above  the  horizon.  This  can  be  easily 
ascertained,  if  we  know  what  is  the  reading  of  the  circle 
when  the  telescope  points  horizontally.  For  example, 
if  the  reading  of  the  circle  is  5°  15'  when  the  telescope 
points  horizontally,  and  27°  16'  25"  when  the  telescope 
is  pointing  to  the  star,  the  telescope  must  point  27°  16' 
25"  —  5°  15' =  22°  i'  25"  above  the  horizon.  The  read- 
ing of  the  circle  when  the  telescope  points  horizontally 
is  ascertained  as  follows.  It  is  well  known  that  a  star 
seen  by  reflection  from  the  surface  of  water  or  quick- 
silver appears  just  as  far  below  the  horizon  as  it  is  above 
it.  The  trough  o  is  filled  with  quicksilver,  and  the  tele- 
scope first  directed  to  a  star,  S  (see  Figure  8),  on  the  me- 

Fig.  8. 


S, 


20  ASTRONOMY. 

ridian,  and  the  reading  of  the  circle  observed ;  the  tele- 
scope is  then  turned  so  as  to  observe  the  star  as  reflected 
by  the  quicksilver,  and  the  reading  of  the  circle  again  ob- 
served. The  horizontal  reading  of  the  circle  is  evidently 
midway  between  these  two  readings. 

The  elevation  of  the  north  celestial  pole  must  next  be 
ascertained.  This  is  done  by  observing  the  Pole  Star. 
This  star,  as  has  already  been  stated,  describes  a  small 
circle  about  the  celestial  pole  as  its  centre.  With  the 
mural  circle  the  angular  elevation  of  this  star  above  the 
horizon  is  observed  at  its  highest  and  lowest  points. 
These  observations  are  corrected  for  refraction,  and  their 
mean  gives  the  angular  elevation  of  the  pole  above  the 
horizon.  The  angular  elevation  of  any  body  above  the 
horizon  is  called  its  altitude,  and  its  altitude  when  on  the 
meridian  is  called  its  meridian  altitude. 

13.  Polar  Distance.  —  By  observing  now  the  altitude 
of  any  star  when  under  the  meridian,  we  can  easily  as- 
certain its  angular  distance  from  the  pole.  This  angular 
distance  is  called  t\\e  polar  distance.  If  the  star  be  north 
of  the  zenith,  its  polar  distance  is  equal  to  the  difference 
between  its  meridian  altitude  and  the  altitude  of  the  pole. 
If  the  star  is  south  of  the  zenith,  its  polar  distance  will 
be  1 80°  minus  the  sum  of  the  altitude  of  the  pole  and 
of  the  meridian  altitude  of  the  star.  This  is  at  once  seen 
by  a  reference  to  Figure  9.  Let  A  Z  B  represent  the 

arc  of  the  meridian  above 
the  horizon.  It  contains, 
of  course,  180°.  Let  P 
represent  the  position  of 
the  pole  whose  altitude 
we  will  suppose  to  be 
42°.  Let  S  be  a  star 
north  of  the  zenith, 
whose  meridian  altitude  is  75°  :  its  polar  distance  P S  = 


ASTRONOMY.  2 1 

75°  —  42°  =  33°.     Let  s  be  a  star  south  of  the  zenith, 
whose  meridian  altitude  H  s  is  45°:  its  polar  distance  P s 

=  180° -(42° +  45°)  =  93°. 

It  is  often  found  more  convenient  to  refer  the  position 
of  the  pole  and  of  the  star  to  the  zenith  rather  than  to 
the  horizon.  The  angular  distance  of  the  pole  or  of  a 
star  from  the  zenith  is  evidently  equal  to  90°  minus  the 
altitude  of  the  pole  or  star. 

14.  Summary.  —  By  means,  then,  of  the  transit  instru- 
ment  and   the  mural   circle,  we  can  determine  the   two 
co-ordinates   necessary   for   describing   the    position   of  a 
star  or  planet  on  the  surface  of  the  sky.     These  co-ordi- 
nates for  the  fixed  stars   are  found  to  be   precisely   the 
same,  whether  they  are  measured  at  Washington,  Green- 
wich, or  the  Cape  of  Good  Hope.     This  shows  that  the 
stars  are  seen  in  exactly  the  same  position,  from  what- 
ever part  of  the  earth  they  are  observed. 

We  have  now  learned  that  the  starry  heavens  appear 
to  rotate,  all  in  a  piece,  from  west  to  east,  once  in  twenty- 
four  hours,  about  an  axis  which  passes  through  the  centre 
of  the  earth  to  a  point  near  the  Pole  Star ;  and  that  the 
fixed  stars,  whether  viewed  from  one  part  of  the  earth  or 
another,  always  appear  in  the  same  parts  of  the  heavens. 

THE  APPARENT   MOTIONS   OF  THE   SUN. 

15.  The  Sidereal  and  the  Solar  Day  and  Year. — We 
have   already  defined  a   sidereal  day  as>  the   interval   of 
time   between   two  successive   transits   of  the   same   star 
across  the  meridian.     The  solar  or  ordinary  day   is  the 
interval  between  two  successive  transits  of  the  sun  across 
the  meridian.      This  interval  is  ascertained  by  means  of 
the   transit  instrument,  in  the  same   way  as   the  interval 
between  the  successive   transits  of  a  given   star.      This 
interval  is  found  to  be  a  little  longer  than  a  sidereal  day. 


2  2  ASTRONOMY. 

If  a  bright  star  which  can  be  seen  with  the  telescope  of 
the  transit  instrument  at  noonday  comes  under  the  me- 
ridian at  precisely  the  same  instant  as  the  sun,  when 
this  star  comes  under  the  meridian  the  next  day,  the  sun 
will  be  about  a  degree  eastward  of  the  meridian  ;  and  the 
next  day,  when  the  star  comes  under  the  meridian,  the 
sun  will  be  about  two  degrees  eastward ;  and  so  on.  In 
about  360  days  after  both  came  under  the  meridian  to- 
gether, they  will  come  under  the  meridian  together  a 
second  time.  When  the  sun  and  a  given  star  come  under 
the  meridian  together,  they  are  said  to  come  into  con- 
junction. The  interval  between  two  successive  conjunc- 
tions of  the  sun  and  a  given  fixed  star  is  called  a  sidereal 
year.  This  year  is  about  2oJ-  minutes  longer  than  the 
ordinary  year.  The  sun,  then,  appears  to  move  entirely 
around  the  heavens,  from  west  to  east  in  a  period  of  about 
one  year.  The  fact  that  the  sun  is  apparently  moving 
eastward  among  the  stars  is  evident  without  the  use  of 
the  transit  instrument.  If  we  notice  the  position  of  the 
constellations  above  the  western  horizon  night  after  night 
at  the  same  time  after  sunset,  we  shall  find  that  they 
come  nearer  and  nearer  the  horizon,  until  many  of  them 
have  disappeared  below  it,  and  we  shall  find,  in _  about  a 
year  from  the  first  observation,  that  these  constellations 
occupy  the  same  position  in  the  heavens  as  at  first. 

One  of  the  co-ordinates  of  the  sun's  position  in  the  sky 
is  daily  changing.  This  co-ordinate  is  the  angular  space 
over  which  the  meridian  must  sweep,  from  a  fixed  point, 
in  order  to  bring  the  sun  on  the  meridian. 

1 6.  The  Solar  Days  are  of  Unequal  Length.  —  Careful 
observation  with  the  transit  instrument  shows  that  the 
sun  is  not  only  apparently  moving  around  the  heavens 
eastward,  but  that  it  is  moving  at  unequal  rates  from  day 
to  day.  The  interval,  therefore,  between  two  successive 
passages  of  the  sun  across  the  meridian  varies  in  length. 


ASTRONOMY.  23 

The  solar  days  are  therefore  of  unequal  length.  The 
solar  day,  like  the  sidereal,  is  divided  into  twenty-four 
equal  parts  called  hours.  The  solar  hours  are  a  little 
longer  than  sidereal  hours,  and  of  unequal  length.  An 
hour  of  ordinary  clock  time  is  the  average  length  of  all 
the  solar  hours;  and  the  ordinary  civil  day,  consisting  of 
twenty-four  hours  of  clock  time,  is  the  average  length  of 
the  solar  days.  Hence  ordinary  clock  time  is  called 
mean  solar  time. 

17.  The  Polar  Distance  of  the  Sun  is  continually  chang- 
ing. —  In  midwinter  the  sun  appears  low  in  the  south, 
and  from  that  time  till  midsummer  its  meridian  altitude 
gradually  increases.  It  then  begins  to  diminish,  and  goes 
on  diminishing  till  midwinter  again.  Now,  since  at  a 
given  place  on  the  earth's  surface  the  altitude  of  the  ce- 
lestial pole1  remains  the  same,  we  must  conclude  that  the 
second  co-ordinate  of  the  sun's  position  in  the  heavens, 
its  polar  distance,  is  continually  changing.  By  means  of 
the  mural  circle  the  least  polar  distance  of  the  sun,  which 
occurs  in  midsummer,  is  found  to  be  about  66 1°,  and  its 
greatest  polar  distance  in  midwinter  is  113^°.  The  circle 
described  by  the  sun  in  its  apparent  journey  round  the 
earth,  then,  is  not  perpendicular  to  the  earth's  axis,  but 
is  inclined  to  that  axis  at  an  angle  of  about  66 J°.  The 
plane  of  the  sun's  orbit  passes  through  the  centre  of  the 
earth,  and  the  circle  formed  by  the  intersection  of  this 
plane  with  the  celestial  sphere  is  called  the  ecliptic. 

When  the  polar  distance  of  the  sun  is  90°,  it  is  directly 
overhead  at  midday  at  the  equator  of  the  earth.  When 
its  polar  distance  is  66 1°,  it  is  directly  overhead  at  mid- 
day at  any  place  23  J°  north  of  the  equator ;  and  when 
its  polar  distance  is  113!°,  it  will  be  directly  overhead  at 
midday  at  any  place  23^°  south  of  the  equator.  At 
every  place,  then,  situated  within  about  23^°  of  the 
equator  either  north  or  south,  —  that  is,  between  the  tropic 


24  ASTRONOMY. 

of  Cancer  and  the  tropic  of  Capricorn,  —  the  sun  comes 
directly  overhead  at  least  once  a  year.  This  belt  of  the 
earth  is  called  the  Torrid  Zane,  ..'^  f 

1 8.  The  Relative  Length  of  Day  and  Night,  and  the 
Changes  of  the  Seasons.  —  The  sun,  of  course,  always  il- 
lumines just  one  half  of  the  earth ;  and  when  the  sun  is 
just  over  the  equator,  the  illumined  part  just  reaches  the 
north  and  the  south  poles.  When  the  sun  is  directly  over 
the  tropic  of  Cancer,  of  course  the  illumined  part  of  the 
earth  reaches  23^°  beyond  the  north  pole,  and  only  to 
within  23  J°  of  the  south  pole.  Hence  an  observer  situated 
within  23^°  of  the  north  pole  would  see  the  sun  during 
the  entire  rotation  of  the  earth,  while  an  observer  within 
23i°  °f  tne  south  pole  would  not  see  the  sun  at  all. 
When  the  sun  is  directly  over  the  tropic  of  Capricorn,  the 
illumined  part  of  the  earth  reaches  23  J°  beyond  the  south 
pole,  and  only  to  within  23^°  of  the  north  pole.  Hence 
a  person  situated  anywhere  within  23^°  of  the  north  pole 
would  not  see  the  sun  at  all  during  twenty-four  hours, 
while  any  person  situated  anywhere  within  23 J°  of  the 
south  pole  would  see  the  sun  the  whole  24  hours.  At 
every  place,  then,  which  is  situated  within  23^°  of  the 
north  or  south  pole,  that  is,  north  of  the  arctic  Or  south 
of  the  antarctic  circle,  there  is  at  least  one  day  in  the 
year  in  which  the  sun  does  not  come  above  the  horizon 
at  all,  and  one  day  in  which  the  sun  does  not  sink  below 
the  horizon  at  all.  The  belts  of  the  earth  betwen  these 
circles  and  the  poles  are  called  the  Frigid  Zones.  Just 
at  the  arctic  and  antarctic  circles  there  is  only  one  day 
in  the  year  in  which  the  sun  does  not  rise  above  or  sink 
below  the  horizon.  But  as  you  go  nearer  the  poles,  the 
number  of  days  when  the  sun  does  not  rise  above  or 
sink  below  the  horizon  increases.  Between  the  arctic 
and  antarctic  circles  and  the  tropics  there  is  no  place 
where  the  sun  comes  directly  overhead,  or  where  it  does 


ASTRONOMY.  25 

not  rise  and  set  every  day.     These  belts  of  the  earth  are 
called  the  Temperate  Zones. 

A  moment's  reflection  will  make  it  clear  that,  when 
the  sun  is  directly  over  the  equator,  every  place  on  the 
surface  of  the  earth  is  illumined  twelve  hours  and  is  in 
darkness  twelve  hours ;  and  as  the  sun  is  directly  over 
the  equator  twice  a  year,  the  days  and  nights  are  equal 
in  every  part  of  the  earth  twice  a  year.  When  the  sun 
is  directly  overhead  at  any  place  north  of  the  equator, 
every  part  of  the  earth  south  of  the  equator  is  in  the  sun- 
shine a  shorter  time  than  it  is  out  of  it,  while  every  place 
north  of  the  equator  is  in  the  sunshine  longer  than  it  is 
out ;  that  is,  in  this  position  of  the  sun  the  days  south  of 
the  equator  are  shorter  than  the  nights,  while  north  of 
the  equator  the  days  are  longer  than  the  nights.  The 
farther  a  place  is  south  of  the  equator,  the  shorter  the 
day  and  the  longer  the  night ;  while  the  farther  north  of 
the  equator  a  place  is,  the  longer  the  day  and  the  shorter 
the  night.  When  the  sun  is  directly  over  any  place  south 
of  the  equator,  the  relative  length  of  the  day  and  night 
is  the  reverse  of  that  just  described ;  that  is,  the  day 
north  of  the  equator  is  shorter  than  the  night,  while 
south  of  the  equator  it  is  longer  than  the  night.  . 

When  the  sun's  north  polar  distance  is  less  than  90°, 
it  is  summer  in  the  northern  hemisphere  and  winter  in 
the  southern,  since  the  northern  hemisphere  then  receives 
more  heat  from  the  sun  than  the  southern.  When  the 
north  polar  distance  of  the  sun  is  more'  than  90°,  it  is 
winter  in  the  northern  hemisphere  and  summer  in  the 
southern,  since  the  latter  then  receives  more  heat  from 
the  sun  than  the  former. 

The  variation  of  the  sun's  polar  distance,  then,  gives 
rise  to  the  change  of  seasons  and  the  varying  length  of 
day  and  night.     If  the  axis  of  the  earth  were  perpendic- 
ular to  the  plane  of  the  sun's  path  among  the  stars,  there 
3 


26  ASTRONOMY. 

would  be  no  change  of  seasons  and  no  variation  in  the 
relative  length  of  day  and  night.* 

19.  Declination  and  Right  Ascension.  —  It  is  often  'con- 
venient to  refer  the  position  of  the  sun  and  stars  to  the 
celestial  equator  rather  than  to  the  celestial  poles.  The 
celestial  equator  is  an  imaginary  circle  perpendicular  to 
the  earth's  axis,  and  dividing  the  celestial  sphere  into  two 
equal  parts. '  The  angular  distance  of  the  sun  or  other 
heavenly  body  from  the  equator,  is  the  difference  between 
90°  and  its  polar  distance.  This  angular  distance  is  called 
decimation ;  north  declination  when  it  is  north  of  the  equa- 
tor, and  south  declination  when  it  is  south  of  the  equator. 
When  the  polar  distance  of  the  sun  is  66J°,  its  declination 
is  23^°  north;  when  its  polar  distance  is  1132°?  its  decli- 
nation is  23^°  south. 

The  plane  of  the  sun's  apparent  orbit  is  evidently  in- 
clined about  23 -i°  to  the  equator,  which  it  bisects. 
Twice  a  year  the  sun's  declination  is  o°.  The  points  at 
which  the  plane  of  the  sun's  orbit  cuts  the  equator  are 
called  equinoctial  points,  since,  as  we  have  already  seen, 
the  days  and  nights  are  equal  in  every  part  of  the  earth 
when  the  sun  is  at  these  points.  The  sun  is  at  one  of 
these  points  on  the  2ist  of  March,  and  at  the  other  on 
the  2ist  of  September.  The  first  point  is  called  the  spring 
or  vernal  equinox,  and  the  second  the  autumnal  equinox. 
The  Spring  equinox  is  not  far  from  Algenib,  a  bright  star 
in  the  constellation  Pegasus ;  and  the  autumnal  equinox  is 
not  far  from  Denebola,  the  bright  star  in  the  tail  of  Leo. 
The  Spring  equinox  is  usually  taken  as  the  fixed  point  on 
the  celestial  sphere  from  which  the  imaginary  meridian  is 
supposed  to  start  in  sweeping  over  the  heavens,  so  as  to 
bring  a  given  star  under  it ;  and  the  angular  distance  which 

*  The  change  of  seasons  and  of  the  relative  length  of  day  and  night 
can  be  more  clearly  illustrated  by  means  of  one  of  the  little  globes 
made  for  that  purpose  than  by  any  description  or  figures. 


,?• 


ASTRONOMY. 

the  meridian  must  sweep  over  from  this  point  to  bring  a 
star  or  planet  under  it  is  called  right  ascension.  Right  as- 
cension is,  therefore,  always  measured  eastward. 

20.  The  Precession  of  the  Equinoxes.  —  It  is  found  that 
the  path  of  the  sun  does  not  always  cross  the  equator  at 
exactly  the  same  place  from  year  to  year.     The  equinoctial 
point  shifts  along  the  equator  westward  50.1"  yearly.     This 
yearly  shifting  of  the  equinoctial  point  is  called  ti\t  preces- 
sion of  the  equinoxes.  <  . 

21.  The  Tropical  Year.  — The  interval  between  two  suc- 
cessive conjunctions  of  the  sun  with  the  same  fixed  star  is 
called,  as  we  have  seen,  a  sidereal year.     The  interval  be- 
tween two  successive  appearances  of  the  sun  at  the  same 
equinoctial  point  is  evidently  a  little  shorter  than  the  si- 
dereal year,   since  this  point  is  continually  shifting  west- 
ward.    This  interval  is  called  a  tropical  year.     It  is  20 J- 
minutes  shorter  than  the  sidereal  year.     The  seasons  are 
evidently  completed  in  a  tropical  year,  since  they  depend 
on  the  declination  of  the  sun.      Hence  the  tropical  year 
is  the  year  of  common  life,  which   is  regulated   by   the 
change  of  the  seasons. 

22.  Solstitial  Points. — When  the  sun  has  reached  his 
greatest  northern  or  southern  declination,  his  declination 
scarcely  changes  for  two  or  three  days.     He  seems  to  halt 
a  little   in  his  journey  toward  the  poles  before  he  turns 
back  toward  the   equator.     These  two  points  in  his  path 
are    called    solstices    (sun-stands').     The    one   north  of  the 
equator,  where  the  sun    appears  in  midsummer,  is  called 
the  summer  solstice;  and  the   one   south  of  the  equator, 
where  the  sun  appears  at  midwinter,  is  called  the  winter 
solstice. 

23.  The  Variation  of  the  Sun's  apparent  Diameter.  —  The 
angular  diameter  of  the  sun  is  about  32',  but  this  diameter 
is  continually  changing.     From  a  certain  point  it  goes  on 
gradually  increasing  for  six  months.      It  then  begins  to 


28  ASTRONOMY. 

diminish,  and  continues  to  diminish  for  the  next  six 
months,  when  it  becomes  the  same  as  at  first.  We  must, 
therefore,  conclude  that  the  sun's  distance  from  the  earth 
is  continually  changing.  It  is  obviously  at  the  greatest 
distance  from  the  earth  when  its  diameter  is  least,  and 
nearest  to  the  earth  when  its  diameter  is  greatest.  It  is  a 
well-known  fact  that  the  angle  subtended  by  any  object  di- 
minishes in  the  same  proportion  as  its  distance  increases. 
If  its  distance  is  doubled,  the  angle  which  it  subtends  is 
diminished  one  half.  Hence,  by  measuring  the  angular 
diameter  of  the  sun  from  time  to  time  we  find  out  the 
relative  distance  of  the  sun  from  the  earth  at  those  times. 
24.  The  Form  of  the  Sun's  apparent  Path  among  the 
Stars.  —  If  we  draw  a  straight  line,  E  A,  to  represent  the 
direction  and  distance  of  the  sun  at  any  time,  and  observe 
the  sun's  angular  diameter  and  his  right  ascension  at  this 
time,  we  can,  by  observing  his  right  ascension  and  angular 
diameter  at  any  other  time,  find  the  length  and  direction 
of  another  line,  E  JB,  which  shall  represent  the  direction 
and  distance  of  the  sun  at  the  time  of  the  second  observa- 
tion. For  the  length  of  the  line  E  B  will  be  to  the  length 
of  the  line  E  A  in  the  inverse  ratio  of  the  observed  angu- 
lar diameters  of  the  sun,  and  the  angle  which  the  line  E  B 
makes  with  E  A  will  evidently  be  the  difference  of  the  ob- 
served right  ascensions. 
In  the  same  way  the 
length  and  direction  of 
the  lines  E  C,  E  D,  E  F, 
E  G,  and  E  H,  are  de- 
termined at  different  times 
in  the  course  of  a  year. 
Now  if  a  curve  be  drawn 
through  the  ends  of  these 
lines,  it  will  evidently 
represent  the  form  of  the 


ASTRONOMY.  2Q 

sun's  path  among  the  stars  during  a  year.  This  curve  is 
found  to  be,  not  a  circle,  but  an  ellipse.  The  earth  is  sit- 
uated at  one  of  the  foci  of  this  ellipse.  The  nearer  the 
sun  is  to  the  earth,  the  more  rapid  is  his  motion  in  right 
ascension. 

25.  Summary. — We  find,   then,   that  the    sun    is   con- 
tinually changing  his  position  with  reference  to  the  fixed 
stars ;  that  he  is  travelling   eastward  among  them  at  the 
rate  of  about  a  degree  a  day,  thus  making  an  entire  cir- 
cuit of  the  heavens  in  a  year.     We  find  that  the  axis  of 
the  earth  is  not  perpendicular  to  this  path,  but  inclined 
to  it  at  an  angle  of  about  66  J° ;  and  that  the  sun  travels 
at  unequal  rates  in  different  parts  of  his  path. 

The  plane  of  the  sun's  path  passes  through  the  earth's 
centre,  and  its  intersection  with  the  celestial  sphere  is 
called  the  ecliptic. 

The  inclination  of  the  earth's  axis  to  the  plane  of  the 
ecliptic  gives  rise  to  the  change  of  seasons  and  the  change 
in  the  relative  length  of  day  and  night. 

TWILIGHT. 

26.  Darkness  does  not  come  on  at  once  after  sunset. 
Full   daylight  gradually  fades  away  into  the  darkness  of 
night,  and  in  the  morning  the  darkness  gradually  melts 
away  into  full  daylight  again.    This  gradual  transition  from 
daylight  to  darkness  in  the  evening,  and  from  darkness  to 
full  daylight  in  the  morning,  is  called  twitight. 

27.  Cause  of  Twilight.  —  After  the  sun  sinks  below  the 
horizon,  it  still  shines  upon  the  particles  of  air  above  the 
earth,  and  these  reflect  the  light  to  the  earth  again.     At 
first  there  is  a  large  number  of  these  illumined  particles 
above  the  horizon,  but  as  the  sun  sinks  lower  and  lower 
they  become  fewer  and  fewer,  and  the  light  which  they > re- 
flect to  the  earth  feebler  and  feebler,  until  it  becomes  im- 

3* 


30  ASTRONOMY. 

perceptible  when  the  sun  has  sunk  18°  below  the  horizon. 
And  again  in  the  morning,  when  the  sun  has  come  within 
1 8°  of  the  horizon,  it  begins  to  shine-  on  the  particles  of 
air  above  the  horizon,  and  they  begin  to  reflect  a  feeble 
light  to  the  earth.  As  the  sun  comes  nearer  and  nearer 
to  the  horizon,  more  and  more  particles  above  the  horizon 
become  illumined,  and  the  light  which  they  reflect  to  the 
earth  becomes  more  and  more  intense,  till  full  daylight 
bursts  forth  at  the  rising  of  the  sun. 

28.  Duration  of  Twilight.  — Twilight,  then,  lasts  at  night 
till  the  sun  is  18°  below  the  horizon,  and  begins  in  the 
morning  when  the  sun  has  come  within  18°  of  the  hori- 
zon. Is  twilight  of  the  same  length  in  different  parts  of 
the  earth,  and  in  the  same  parts  of  the  earth  at  different 
seasons  of  the  year?  This  is  equivalent  to  inquiring 
whether  the  sun  gets  18°  below  the  horizon  in  the  same 
time  in  different  parts  of  the  earth,  or  in  the  same  part  of 
the  earth  at  different  seasons.  When  we  say  that  the  sun 
is  18°  below  the  horizon,  we  mean  18°  measured  on  a  ver- 
tical circle,  that  is,  a  circle  perpendicular  to  the  horizon 
and  passing  through  the  zenith.  We  will  suppose  the  time 
to  be  the  2ist  of  March,  and  the  place  to  be  the  equator 
of  the  earth.  Here  the  circle  described  by  the  sun  in  his 
apparent  daily  motion  is  perpendicular  to  the  horizon  and 
passes  through  the  zenith,  that  is,  it  is  a  vertical  circle ; 
and  when  the  earth  has  rotated  through  18°  after  the  sun 
has  reached  the  horizon,  he  will  be  18°  below  it,  and  twi- 
light will  end.  We  will  next  suppose  the  time  to  be  the 
same,  but  the  observer  to  be  either  north  or  south  of  the 
equator.  The  circle  described  by  the  sun  in  his  apparent 
daily  motion  is  still  a  great  circle,  but  it  is  inclined  to  the 
horizon,  and  so  is  not  a  vertical  circle.  The  sun  here  will 
evidently  not  be  18°  below  the  horizon  when  the  earth  has 
rotated  18°  after  the  sun  has  reached  the  horizon.  For 
the  sun  has  gone  down  obliquely  below  the  horizon,  and 


ASTRONOMY.  3 1 

he  must  descend  more  than  18°  degrees  in  this  oblique 
path  in  order  to  get  18°  below  the  horizon;  just  as  one  in 
walking  obliquely  from  a  wall  must  ^walk  more  than  ten 
feet  to  get  ten  feet  from  the  wall.  Hence  when  the  sun  is 
on  the  equator,  twilight  is  shorter  at  the  equator  than  at 
places  north  or  south  of  the  equator.  The  farther  north 
or  south  of  the  equator,  the  more  obliquely  does  the  sun 
rise  and  set,  and  of  course  the  longer  the  twilight. 

We  will  next  suppose  that  the  sun  is  at  the  summer  or 
winter  solstice,  and  that  the  observer  is  at  the  equator. 
The  diurnal  path  of  the  sun  is  still  perpendicular  to  the 
horizon,  but  does  not  pass  through  the  zenith.  It  is  not 
a  great  circle,  but  a  small  circle.  When,  therefore,  the 
earth  has  rotated  18°  after  the  sun  has  reached  the  hori- 
zon, the  sun  is  not  18°  below  the  horizon,  since  an  arc  of 
1 8°  on  a  small  circle  is  shorter  than  an  arc  of  18°  on  a 
vertical  circle,  which  is  a  great  circle.  Hence  twilight  at 
the  equator  grows  longer  as  the  sun  passes  north  or  south 
of  the  equator. 

Suppose  now  that  an  observer  is  north  of  the  equator, 
and  the  sun  is  at  one  of  the  solstices.  The  plane  of  the 
horizon  is  now  inclined  to  the  axis  of  the  earth's  rotation, 
and  is  carried  around  that  axis  with  a  wabbling  motion. 
This  motion  may  be  illustrated  by  passing  a  wire  through 
the  centre  of  a  piece  of  cardboard,  and  fastening  the  card 
so  that  it  will  be  inclined  to  the  wire,  and  then  rotating 
the  wire. 

Let  us  first  see  what  would  be  true  of  twilight,  provided 
the  horizon  were  rotating  on  an  axis  which  coincided  with 
its  own  plane.  When  the  sun  is  either  north  or  south  of 
the  equator,  its  daily  motion  is  in  a  small  circle,  and  as 
these  small  circles  are  all  equally  inclined  to  the 'plane  of 
the  horizon,  twilight  would  grow  longer  as  these  circles 
become  smaller ;  that  is,  as  the  sun  moves  north  and  south 
from  the  equator.  But  by  referring  to  the  illustration  of 


32  ASTRONOMY. 

the  wabbling  motion  of  the  plane  of  the  horizon  in  conse- 
quence of  its  being  inclined  to  the  axis  of  the  earth's  rota- 
tion, it  will  be  seen  that  to  a  person. north  of  the  equator 
the  portion  of  the  heavens  south  of  the  east  and  west 
points  is  carried,  as  it  rotates,  bodily  away  from  the  stars  as 
they  sink  below  it ;  while  the  portion  north  of  those  points 
is  carried  bodily  towards  the  stars  as  they  sink  below  it. 
Thus  this  wabbling  motion  of  the  horizon  tends  to  increase 
the  length  of  twilight  in  summer,  and  to  shorten  it  in  win- 
ter ;  while  the  fact  that  the  sun  is  moving  in  small  circles 
at  each  of  these  times  tends  to  increase  the  length  of  twi- 
light as  well  in  winter  as  in  summer.  The  tendency  of 
this  wabbling  motion  of  the  horizon  to  diminish  the  length 
of  twilight  in  winter,  in  our  latitude,  almost  exactly  balan- 
ces the  effect  of  the  sun's  moving  in  a  small  circle.  The 
length  of  twilight  varies  but  a  few  minutes  from  the  au- 
tumnal to  the  vernal  equinox ;  while  in  midsummer  in  our 
latitude,  twilight  is  half  an  hour  longer  than  at  the  equi- 
noxes. At  the  poles  the  sun  never  sinks  more  than  23^° 
below  the  horizon,  hence  the  twilight  there  lasts  about  two 
thirds  of  the  long  winter  night. 

29.  Summary. — The  twilight  at  the  equator  is  shortest 
when  the  sun  is  on  the  equator,   and  longest  when  the 
sun  is  farthest  north  or  south  of  the  equator.     The  short- 
est twilight  at  any  time  is  at  the  equator. 

As  you  go  from  the  equator  either  north  or  south,  the 
twilight  lengthens,  and  it  is  longer  in  summer  than  in  win- 
ter. The  shortest  twilight  at  the  equator  is  about  one 
hour  and  twelve  minutes ;  in  our  latitude  it  is  about  an 
hour  and  a  half. 

THE*  APPARENT  MOTION   OF  THE   MOON. 

30.  The  Lunar  Month.  —  The  new  moon  is  always  seen 
near  the  western  horizon  soon  after  sunset.     It  is  farther 


ASTRONOMY.  33 

and  farther  from  the  horizon  at  sunset,  night  after  night, 
until  about  a  fortnight  from  new  moon,  when  the  moon 
becomes  full  and  rises  just  as  the  sun  sets.  It  then  lags 
farther  and  farther  behind  the  sun  until  it  does  not  rise  till 
just  before  sunrise. 

We  see,  then,  that  the  moon  is  also  moving  eastward 
among  the  stars,  and  that  it  is  moving  more  rapidly  than 
the  sun.  When  the  moon  and  sun  both  rise  or  set  to- 
gether, they  are  said  to  be  in  conjunction;  and  when  the 
moon  rises  just  as  the  sun  sets,  it  is  said  to  be  in  opposi- 
tion. The  moon  passes  from  conjunction  to  conjunction, 
or  from  opposition  to  opposition,  in  29  J  days.  This  period 
is  the  ordinary  lunar  month. 

The  moon,  like  the  sun,  in  her  eastward  journey  among 
the  stars,  changes  not  only  her  right  ascension  from  day  to 
day,  but  also  her  declination.  The  points  at  which  the 
moon's  path  cuts  the  ecliptic  are  called  the  nodes  (knots). 
The  point  where  its  path  cuts  it  from  south  to  north  is 
called  the  ascending  node,  while  the  other  is  called  the 
descending  node. 

3 1.  The  Lunar  Day.  —  The  interval  between  two  succes- 
sive passages  of  the  moon  across  the  meridian  is  sometimes 
called  a  lunar  day.     This  interval  is  nearly  an  hour  longer 
than  the  solar  day.     The  lunar  days  are  found  to  be  even 
more  unequal  in  length  than  the  solar  days. 

32.  The  Moon's  Orbit  is  an  Ellipse.  — By  a  method  sim- 
ilar to  that  used  in  the  case  of  the  sun,  the  orbit  of  the 
moon  is  found  to  be  an  ellipse,  which  has»the  earth  at  one 
of  its  foci.     When  the  moon  is  in  that  part  of  her  orbit 
which  is  nearest  to  the  earth,  she  is  said  to  be  in  perigee 
(near  the  earth),  and  when  in  that  part  of  her  orbit  farthest 
from  the  earth,  she  is  said  to  be  in  apogee  (away  from  the 
earth).     The  line  joining  these  points  of  the  moon's  orbit 
is  the  major  axis  of  an  ellipse,  and  is  called  the  line  of 
apsides.     The  moon  moves  faster  at  perigee  than  at  apogee. 


34  ASTRONOMY. 


THE  APPARENT  MOTIONS  OF  THE  PLANETS. 

33.  Venus.  — There  is  a  conspicuous  star  sometimes  seen 
in  the  west  in  the  early  evening,  and  sometimes  in  the  east 
before  sunrise.     This  star  is  familiarly  known  as  the  morn- 
ing and  evening  star.     If  it  be  watched  for  some  time  it 
will  be  seen,  after  it  has  ceased  to  be  a  morning  star,  close 
to  the  horizon  in  the  west  soon  after  sunset.     Then  night 
after  night  it  will  be  seen  to  have  moved  farther  and  far- 
ther to  the  eastward  from  the  sun,  until  its  angular  dis- 
tance from  him  is  about  47°.     Venus,  at  this  point,  is  said 
to  be  at  its  greatest  eastern  elongation  from  the  sun.     It 
then  begins  to  approach  the  sun,  and  finally  passes  him 
and  appears  again  on  his  western  side  as  a  morning  star. 
It  separates  farther  and  farther  from  him  to  the  westward, 
until  its  angular  distance  from  him  is  again   about  47°, 
when  it  is  said  to  be  at  its  greatest  western  elongation 
from  the  sun.       It  then   approaches  the  sun  again,   and 
passes  by  him  to  the  eastward.     The  interval  between  two 
successive  appearances  of  Venus  at  its  greatest  eastern  or 
its  greatest  western  elongation  is  about  nineteen  months. 
We  see,  then,  that  Venus  is  apparently  carried  on  with  the 
sun  in  his   eastward  journey  among  the  stars,  sometimes 
falling  behind  him  an  angular  distance  of  47°,  and  again 
overtaking  and  passing  beyond  him  a  like  distance. 

34.  Mercury.  —  The  movements  of  Mercury  are  similar 
to  those  of  Venus,  but  his  greatest  elongation  from  the  sun 
never  exceeds  29°,  so  that  he  sinks  below  the  horizon  too 
soon  after  sunset,  and  rises  too  short  a  time  before  the 
sun,  to  be  often  visible  to  the  naked  eye. 

Stars,  like  Mercury  and  Venus,  which  are  thus  continu- 
ally changing  their  position  in  the  sky,  are  called  planets 
(wanderers),  to  distinguish  them  from  the  fixed  stars,  which 


ASTRONOMY.  35 

we  have  seen  do  not  sensibly  change  their  position  in  the 
sky. 

35.  Movements  of  the  other  Planets  among  the  Stars. — 
Besides  the  two  planets,  Mercury  and  Venus,  there  are 
three  other  planets,  Mars,  Jupiter,  and  Saturn,  which  are 
conspicuous  to  the  naked  eye ;  and  two  large  planets,  Ura- 
nus and  Neptune,  which  are  so  distant  that  they  cannot  be 
seen  except  with  the  telescope ;  and  a  large  number  of 
smaller  ones,  called  asteroids,  which,  though  nearer,  can 
be  seen  only  with  a  telescope. 

If  one  of  the  most  conspicuous  of  these  planets,  as  Ju- 
piter, be  watched  for  a  series  of  years,  it  will  be  found  to 
work  its  way  gradually  to  the  eastward  among  the  stars, 
and  to  complete  the  circuit  of  the  heavens  in  a  longer  or 
shorter  time.  This  time  is  found  to  be  always  the  same 
for  the  same  planet ;  but  different  for  different  planets. 
But  this  eastward  motion  of  the  planet  is  not  regular  and 
uniform.  The  planet  advances  quite  rapidly  at  times,  then 
halts  and  remains  stationary,  then  actually  goes  backward 
or  retrogrades,  then  halts  and  remains  stationary  again, 


and  again  advances. 


Fig.  n. 


Figure  n  represents  the  apparent  motion  of  Jupiter 
among  the  stars  during  the  year  1866. 

THE   PTOLEMAIC    SYSTEM. 

36.  We  have  now  seen  that  the  sun  appears  to  revolve 
about  the  earth  from  west  to  east  once  in  a  year  in  an 
orbit  whose  exact  form  is  an  ellipse  ;  that  the  moon  ap- 
pears to  revolve  about  the  earth  in  the  same  direction 
and  in  an  orbit  of  the  same  form  once  in  a  month-;  that 


36  ASTRONOMY. 

Mercury  and  Venus  appear  to  swing  backward  and  for- 
ward across  the  sun,  while  they  are  at  the  same  time  car- 
ried onward  with  him  in  his  eastward  motion ;  and  that 
the  other  planets  also  appear  to  move  about  the  earth  in 
longer  or  shorter  periods  and  in  very  irregular  paths.  It 
seems  improbable  that  any  planet  should  really  move  in  so 
irregular  a  path  as  Jupiter  appears  to  move  in. 

The  ancient  astronomers  assumed  that  the  planets  all 
moved  in  circular  orbits,  and  attempted  to  account  for 
their  apparent  irregular  motions  by  the  combination  of 
various  circular  motions.  They  supposed  that  the  earth  is 
fixed,  and  that  the  sun  moves.  They  supposed  that  a  bar, 
or  something  equivalent,  was  connected  at  one  end  with 
the  earth,  and  that  on  some  part  it  carried  the  sun ;  and  as 
they  saw  that  the  planet  Venus  is  apparently  sometimes 
on  one  side  of  the  sun  and  sometimes  on  the  other,  they 
said  that  the  planet  Venus  moves  in  a  circle  whose  centre 
is  on  the  same  bar.  Then  if  we  suppose  that  Venus  is  re- 
volving around  this  centre  at  the  same  time  that  the  bar 
is  moving  about  the  earth,  we  get  a  perfect  representa- 
tion of  the  apparent  motion  of  Venus  and  the  sun  as  seen 
from  the  .earth.  This  is  illustrated  by  Figure  12.  Sup- 


Fig.  12. 


pose  E  to  be  the  fixed  earth  ;  E  v  S  m  n,  a  bar  turning  in 
a  circle,  having  one  end  fixed  at  E ;  S  the  sun  carried  by 
it ;  vy  the  centre  of  the  orbit  in  which  Venus  revolves ; 


ASTRONOMY.  37 

V,  the  planet  Venus,  connected  with  v  by  a  bar  (real  or 
imaginary),  and  thus  describing  a  circle  round  v,  while  v 
itself  is  carried  on  the  bar  round  the  earth. 

It  was  supposed  that  Mercury  revolved  in  another  cir- 
cle, whose  centre  was  also  on  the  same  bar,  but  perhaps 
beyond  the  sun,  as  at  m.  They  did  not  pretend  to  say 
exactly  where  these  centres  were  :  all  that  they  were  cer- 
tain about  was  this;  that  the  centre  of  motion  of  each 
planet  was  on  the  same  bar  that  supported  the  sun.  Now 
it  is  easy  to  be  seen,  on  these  suppositions,  that  both 
Mercury  and  Venus  would  appear,  when  viewed  from  the 
earth,  at  one  time  on  the  right  and  again  on  the  left  of 
the  sun,  and  at  the  same  time  they  would  appear  to  be 
carried  around  the  earth  with  him. 

With  regard  to  Mars,  they  found  out  that  its  motion 
could  be  represented  pretty  well  by  supposing  that  this 
same  bar  carried  another  centre  at  n,  around  which  Mars 
revolved  as  at  Ma,  carried  by  an  arm  long  enough  to 
project  beyond  the  earth,  so  that  its  orbit  completely  sur- 
rounded the  earth  as  well  as  the  sun.  In  the  same  way 
the  apparent  motions  of  Jupiter  and  Saturn  were  ac- 
counted for. 

The  motion  of  the  planet  Mars,  however,  still  pre- 
sented some  discordances,  and  there  were  some  smaller 
discordances  with  regard  to  all  the  other  planets.  These 
led  to  the  invention  of  those  things  known  as  epicycles, 
deferents,  etc.,  the  nature  of  which  may  be  thus  ex- 
plained. By  the  contrivance  which  we  have  already  de- 
scribed, they  found  that  the  movement  of  the  point  Ma 
at  the  end  of  the  rod  n  Ma  would  nearly,  but  not  ex- 
actly, represent  the  motion  of  Mars.  To  make  it  repre- 
sent the  motion  more  exactly,  they  supposed  that  another 
small  rod,  Ma  N,  was  carried  by  the  longer  rod,  jointed  at 
Ma,  and  turning  around  in  a  different  time.  To  make  it 
still  more  exact,  they  supposed  another  shorter  rod  car- 
4 


38  ASTRONOMY. 

ried  at  JV,  and  that  its  extremity  carried  the  planet  Mars. 
The  same  complications  were  necessary  for  all  the  other 
planets.  It  will  be  thus  seen  that  a  combination  of  no 
less  than  five  circular  motions  was  necessary  to  account 
for  the  apparent  irregularities  in  the  motion  of  a  single 
planet.  Thus  the  joint  n  moved  in  a  circle  about  E ;  the 
joint  'Ma  in  a  circle  about  n;  the  joint  JV  about  Ma  ;  and 
the  planet  Mars  about  N.  Of  all  the  complicated  sys- 
tems that  man  ever  devised,  there  never  was  one  like 
this  Ptolemaic  system.  The  celebrated  king  of  Castile, 
Alfonso,  the  greatest  patron  of  astronomy  in  his  age, 
alluding  to  this  theory  of  epicycles,  said  that  "  if  he  had 
been  consulted  at  the  creation,  he  could  have  done  the 
thing  better." 

THE   SYSTEM   OF   TYCHO   DE   BRAHE. 

37.     If  we  suppose  the  earth  fixed  as  at  E  (Figure  13), 
and   Venus    to    be    revolving    around   a    centre    situated 

somewhere  in  the  line  E  £, 
we  may  remove  that  cen- 
tre as  far  from  the  earth  as 
we  please,  and  yet  get  the 
same  appearance,  provided 
we  enlarge  the  dimensions 
of  the  orbit  of  Venus  in  the 
same  .  proportion.  For  in- 
stance, suppose  E  to  be  the 
earth,  the  smaller  circle  to  be  the  orbit  of  Venus,  and  the 
sun  to  be  at  S  ;  then,  in  revolving  in  her  orbit,  Venus  will 
appear  to  go  to  a  certain  distance  to  the  right  and  to  the 
left  of  the  sun.  But  we  may  take  any  other  point  on  the 
bar,  even  the  point  S  itself,  as  the  centre  of  the  orbit  of 
Venus,  provided  we  give  Venus  a  larger  circle  to  revolve 
in.  If  the  larger  circle  in  the  figure  represents  the  orbit 


ASTRONOMY. 


39 


of  Venus,  she  will  appear  to  move  just  as  far  to  the  right 
and  to  the  left  of  the  sun  as  when  she  moved  in  the  small 
orbit.  We  may  then  fix  the  centre  of  the  orbit  of  Venus 
where  we  please ;  and  so  with  the  centres  of  the  orbits 
of  Mercury,  Mars,  and  of  each  of  the  other  planets,  pro- 
vided we  give  proper  dimensions  to  their  orbits.  By  hav- 
ing all  their  centres  at  the 
centre  of  the  sun,  we  have 
all  the  planets  revolving 
about  the  sun,  while  the 
sun  revolves  about  the 
earth,  as  shown  in  Figure 
14.  This  system  is  much 
less  complex  than  the 
Ptolemaic  system,  though 
the  theory  of  epicycles 
and  deferents  is  still  re- 
tained. This  modification 
of  the  Ptolemaic  system 

was  adopted  by  the  great  Danish  astronomer,  Tycho  de 
Brahe. 


THE   COPERNICAN   SYSTEM. 

38.  Now,  instead  of  supposing  the  sun  to  be  travelling, 
and  by  some  imaginary  power  causing  the  planets  to  re- 
volve about  himself  as  their  travelling  centre,  suppose  we 
say  that  the  earth  revolves  about  the  sun,  and  that  the 
sun  is  a  fixed,  or  nearly  fixed,  body,  and  that  all  the 
planets,  including  the  earth,  go  around  the  sun ;  that  is, 
in  Figure  14,  instead  of  supposing  S  with  the  whole  sys- 
tem of  orbits  to  be  travelling  around  £,  suppose  Me,  V, 
E.  and  Ma  to  travel  in  separate  orbits  about  S,  and  the 
appearances  of  the  planets,  as  viewed  from  the  earth,  will 
be  represented  exactly  as  well  as  before. 


40  ASTRONOMY. 

This  great  step  of  assuming  the  sun  to  be  the  centre 
of  motion  of  all  the  planets,  including  the  earth,  was 
taken  by  Copernicus.  But  he  could-  not  get  rid  of  the 
epicycles  to  account  for  the  apparent  irregularities  in  the 
motion  of  the  planets. 

THE   SYSTEM   OF   KEPLER. 

39.  Tycho  de  Brahe  had  employed  a  good  part  of  his 
life  in  observing  and  recording  the  position  of  the  heav- 
enly bodies.  His  pupil,  Kepler,  by  examining  carefully 
the  observations  which  Brahe  had  made  of  the  planets, 
and  especially  of  the  planet  Mars,  and  comparing  them 
with  his  own,  ascertained  that  the  whole  could  be  repre- 
sented with  the  utmost  accuracy  by  supposing  that  Mars 
moves  in  an  ellipse,  one  of  whose  foci  is  occupied  by  the 
sun.  It  is  difficult  to  explain  in  a  few  words  how  Kepler 
came  to  this  conclusion ;  generally  speaking,  it  was  by 
the  method  of  trial  and  error.  The  number  of  supposi- 
tions he  made  to  account  for  the  motion  of  the  planets 
is  beyond  belief:  that  the  planets  turned  round  centres 
at  a  little  distance  from  the  sun ;  that  their  epicycles  and 
deferents  turned  on  points  at  a  little  distance  from  the 
ends  of  the  bar  to  which  they  were  jointed ;  and  the 
like.  After  trying  every  device  he  could  think  of  with 
epicycles,  eccentrics,  and  deferents,  and  computing  the 
apparent  place  of  Mars  from  these  different  assumptions, 
and  comparing  them  with  the  places  really  observed  by 
Brahe,  he  found  that  he  could  not  bring  them  nearer  to 
Brahe's  observations  than  eight  minutes  of  a  degree.  He 
then  said  boldly  that  so  good  an  observer  as  Brahe  could 
not  be  wrong  by  eight  minutes,  and  added,  "  Out  of  these 
eight  minutes  we  will  construct  a  new  theory  that  will 
explain  the  motion  of  all  the  planets."  The  theory  thus 
constructed  was,  that  all  the  planets  move  in  ellipses 


ASTRONOMY.  41 

which  have  the  sun  at  one  of  their  foci.  This  theory 
has  been  found  to  explain  accurately  all  the  seeming  ir- 
regularities in  the  motion  of  the  planets. 

The  planets  appear  to  advance  and  retrograde  because 
they  are  seen  from  the  earth,  which  is  itself  revolving 
about  the  sun.  If  they  were  seen  from  the  sun,  their 
advance  would  be  steady  and  regular. 

To  construct  an  ellipse,  stick  two  pins  into  a  board  a 
little  way  apart;  fasten  to  the  pins  the  ends  of  a  string 
somewhat  longer  than  the  distance  between  the  pins ;  then, 
keeping  the  string  stretched  by  the  point  of  a  pencil, 
carry  the  pencil  round.  The  curve  described  will  be  an 
ellipse,  and  the  points  where  the  pins  are  stuck  into  the 
board  will  be  the  foci  of  the  ellipse. 

If  the  ellipse  in  Figure  15  be  the  orbit  of  a  planet,  6* 
will  be  the  place  of  the  sun.  The  sun 
is  at  the  focus  of  the  ellipse  described 
by  every  planet.  Every  planet  describes 
a  different  ellipse.  The  degree  of  flat- 
ness of  the  ellipse  is  different  for  every 
planet,  and  the  direction  of  the  long 
diameter  of  the  ellipse  is  different  for 
every  planet.  There  is,  in  fact,  the 
greatest  variety  among  the  ellipses  de- 
scribed by  the  different  planets. 

40.  Kepler's  First  Law.  —  The   first   great   fact,    then, 
that  Kepler  made  out  with  regard  to  the  motion  of  the 
planets   is,   that  they  all  move  in  ellipses,  which  have  the 
sun   at  one  focus.     This   fact  is    usually   called     Kepler's 
first  law. 

41.  Kepler's  Second  Law.  —  The  second  fact  made  out 
by  this  astronomer  is,  that  the  planets  move  at  unequal 
rates  in   different  parts  of  their  orbits.      He   found   that 
each  planet,  when  in  its  perihelion,  that  is,  the  part  of  its 
orbit  which  is  nearest  the  sun,  travels  quickly,  and  when 

4* 


42  ASTRONOMY. 

in  its  aphelion,  or  the  part  of  its  orbit  which  is  farthest 
from  the  sun,  travels  slowly. 

Kepler  expressed  this  law  of  motion  in  this  way :  if  in 
one  part  of  the  planet's  orbit  the  lines  S  K  and  SL  (see 
Figure  15)  enclose  a  certain  portion  of  the  area  of  the 
ellipse,  and  in  another  part  the  two  lines  s  k  and  s  I  en- 
close a  space  equal  to  that  enclosed  by  S  K  and  S  L,  the 
planet  will  be  just  as  long  in  moving  over  the  short  arc 
k  I  as  over  the  large  arc  K  L  ;  that  is,  the  planets  describe 
equal  areas  in  equal  times. 

42.  Kepler's  Third  Law.  —  Kepler  made  out  another 
very  important  fact  with  regard  to  the  motions  of  the 
planets  compared  with  their  distances  from  the  sun ; 
namely,  that  the  squares  of  the  periodic  times  of  the  plan- 
ets are  to  each  other  as  the  cubes  of  their  mean  distances  from 
the  sun. 


SUMMARY. 

The  earth,  sun,  moon,  and  planets  are  globes.  The 
shape  of  the  fixed  stars  is  unknown.  (2,  3.) 

The  starry  heavens  appear  to  rotate  in  a  piece  from 
east  to  west  about  an  axis  which  passes  through  the 
centre  of  the  earth  and  a  point  near  the  Polar  Star. 
This  rotation  is  completed  in  twenty-four  hours.  (6.) 

The  earth  rotates  from  west  to  east  once  in  twenty- 
four  hours  about  an  axis  which  passes  through  the  cen- 
tre of  the  earth  and  a  point  near  the  Polar  Star.  This 
rotation  of  the  earth  causes  the  heavens  to  appear  to 
rotate  in  the  opposite  direction.  (8.) 

The  stars  describe  accurate  circles,  though  their  paths 
are  somewhat  disturbed  by  refraction.  (5,  7.) 

The  circles  described  by  the  stars  are  differently  in- 
clined to  the  plane  of  the  horizon  in  different  parts  of 
the  earth.  (9.) 


ASTRONOMY.  43 

The  co-ordinates  of  a  heavenly  body  are  the  angular 
distance  of  the  body  from  the  celestial  pole,  and  the 
angular  distance  that  the  meridian  must  sweep  over  from 
a  fixed  point  to  bring  the  body  under  it.  (10.) 

The  latter  of  these  co-ordinates  is  measured  by  means 
of  the  Transit  Instrument ;  the  former,  by  means  of  the 
Mural  Circle,  (n,  12.) 

The  co-ordinates  of  the  fixed  stars  are  always  the 
same  wherever  they  are  measured.  (14.) 

The  co-ordinates  of  the  sun  ^.re  found  to  change  daily. 
He  travels  eastward  among  the  stars  and  completes  the 
circuit  of  the  heavens  once  a  year. 

The  plane  of  his  orbit  passes  through  the  centre  of 
the  earth,  and  is  inclined  to  the  earth's  axis  at  an  angle 
of  661°.  (15,  17.) 

The  sun  in  his  eastward  journey  describes  an  ellipse 
with  the  earth  at  one  of  its  foci.  (24.) 

The  moon  travels  eastward  among  the  stars  more  rap- 
idly than  the  sun.  She  completes  a  circuit  of  the  heav- 
ens in  a  month,  and  describes  an  ellipse  with  the  earth 
at  its  focus.  (30,  32.) 

Venus  and  Mercury  are  seen  to  vibrate  to  and  fro 
across  the  sun.  At  their  greatest  elongations,  Venus  is 
47°,  and  Mercury  29°,  from  the  sun.  (33,  34.) 

The  other  planets  describe  very  circuitous  paths  among 
the  stars.  They  advance  to  the  eastward  for  a  time,  then 
halt,  and  then  even  go  backward.  (35-) 

The  ancient  astronomers  assumed  that'  the  planets  all 
moved  in  circular  orbits,  and  attempted  to  account  for 
their  apparent  irregular  motion  by  the  combination  of 
various  circular  motions.  They  constructed  a  system  of 
cycles,  epicycles,  and  deferents.  (36.) 

Tycho  de  Brahe  simplified  the  Ptolemaic  system  by 
placing  the  centres  of  all  the  cycles  at  the  centre  of  the 
sun.  (37.) 


44  ASTRONOMY. 

Copernicus  simplified  it  further  by  making  the  earth 
revolve  about  the  sun.  (38.) 

Kepler  was  the  first  who  did  away  with  the  complex 
system  of  cycles  and  epicycles  by  showing  that  all  the 
planets  move  in  ellipses,  all  of  which  have  the  sun  at  one 
focus.  (39,  40.) 

He  further  showed  that  the  planets  describe  equal  areas 
in  equal  times,  and  that  the  squares  of  the  periodic  times 
of  the  planets  are  to  each  other  as  the  cubes  of  their  mean 
distances  from  the  sun.  (4%  42.) 

A  sidereal  day  is  the  interval  between  two  successive 
transits  of  a  star  across  the  meridian. 

The  solar  day  is  the  interval  between  two  successive 
transits  of  the  sun  across  the  meridian.  (15.) 

The  solar  days  are  of  unequal  length.  The  ordinary 
civil  day  is  the  average  length  of  these.  (16.) 

The  variation  of  the  sun's  polar  distance  gives  rise 
to  the  change  of  seasons  and  the  varying  length  of  day 
and  night.  (18.) 

The  circle  formed  by  the  intersection  of  the  plane  of  the 
sun's?  orbit  with  the  celestial  sphere  is  called  the  ecliptic. 

The  celestial  equator  is  a  circle  which  is  perpendicular 
to  the  earth's  axis  and  which  divides  the  celestial  sphere 
into  two  equal  parts. 

The  points  where  the  sun's  orbit  cuts  the  celestial 
equator  are  called  the  equinoxes. 

Angular  distance  measured  north  or  south  from  the 
celestial  equator  is  called  declination. 

Angular  distance  measured  from  the  vernal  equinox 
eastward  is  called  right  ascension.  (19.) 

The  equinoxes  slowly  shift  along  the  equator  to  the 
westward.  This  shifting  is  called  the  precession  of  the 
equinoxes.  (20.) 

The  interval  between  two  successive  conjunctions  of 
the  sun  with  the  same  fixed  star  is  a  sidereal  year. 


ASTRONOMY.  45 

The  interval  between  two  successive  appearances  of 
the  sun  at  the  same  equinox  is  a  tropical  year.  (21.) 

The  points  in  the  sun's  path  at  which  he  gains  his 
greatest  northern  or  southern  declination  are  called  the 
solstices.  (22.) 

Twilight  is  caused  by  the  reflection  of  the  sun-light 
from  the  clouds  and  the  particles  of  air. 

It  continues  while  the  sun  is  within  18°  of  the  hori- 
zon. It  is  shortest  at  the  equator  and  longest  at  the 
poles.  In  our  latitude  it  is  longer  in  the  summer  than 
in  the  winter.  (27.) 


HOW  TO   FIND   THE   PERIODIC   TIMES   OF 
THE   PLANETS. 

43.  The  Periodic  time  of  the  Earth  determined  by  direct 
Observation.  —  We  have  seen  that  the  real  motion  of  the 
earth  about  the  sun  causes  the  sun  to  appear  to  revolve 
about  the  earth.     It  is  evident  that  the  time  that  it  takes 
the  earth  to  revolve  about  the   sun  is  the  same  as » that 
which  it  takes  the  sun  to  make   an  apparent  revolution 
around   the    earth.      The   periodic   time   of  the   earth   is 
found  by  observing  the  interval  between  two  successive 
appearances  of  the  sun  at  the  same  equinox,  or  two  suc- 
cessive conjunctions  with  the  same  star. 

44.  Synodic  Period  of  a  Planet  determined  by  direct  Ob- 
servation. — 'The  planets  Venus  and  Mercury,  as  we  have 
already  seen,  never  appear  in   the   part  of  the  heavens 
opposite   to  the   sun.     Hence  the  orbits  of  these  planets 
must  lie    wholly   inside    the    orbit    of  the    earth.      When 
these  planets   come  between  the  earth  and  the  sun  they 
are  said  to  be  in  inferior  conjunction,  and  when  the  sun  is 
between  them  and  the  earth  they  are  said  to  be  in  supe- 
rior conjunction.       The   planets   whose   orbits   lie   wholly 


46  ASTRONOMY. 

within  the  earth's  orbit  are  called  inferior  planets.  Those 
whose  orbits  lie  wholly  without  the  earth's  orbit  are  called 
superior  planets.  When  a  superior  planet  appears  in  the 
same  part  of  the  heavens  as  the  sun,  that  is,  when  the 
sun  is  between  the  earth  and  planet,  it  is  said  to  be  in 
conjunction.  When  the  planet  appears  in  the  opposite 
part  of  the  heavens  to  that  of  the  sun,  that  is,  when  the 
earth  is  between  the  planet  and  the  sun,  it  is  said  to  be 
in  opposition. 

The  interval  between  two  successive  oppositions  of  a 
planet,  or  between  two  successive  conjunctions  of  the 
same  kind,  is  called  the  synodic  revolution  of  the  planet. 
This  interval  is  determined  by  direct  observation. 

45.  Hoiv  to  find  the  Sidereal  Period  of  an  inferior  Planet. 
—  The  sidereal  period  of  a  planet  is  the  time  it  takes  to 
make  a  complete  revolution  about  the  sun.  This  time 
can  be  easily  computed  when  we  know  the  sidereal  period 
of  the  earth  and  the  synodic  period  of  the  planet. 

Let  P  be  the  sidereal  period  of  the  earth,  S  the  sy- 
nodic period  of  Venus,  and  /  the  sidereal  period  of  Venus. 
P  and  S  are  known  by  direct  observation,  and  /  is  re- 
quired. 

We  will  suppose  that  Venus  is 
at  inferior  conjunction ;  then  £, 
V,  and  S  will  represent  the  re- 
spective places  of  the  earth,  Ve- 
nus, and  the  sun.  If  the  earth 
were  stationary  as  well  as  the  sun, 
then  Venus  would  come  again  into 
conjunction  when  it  had  just  com- 
pleted a  revolution  about  the  sun ;  but  the  earth  is  mov- 
ing in  the  same  direction  as  Venus,  hence  Venus  must 
make  a  complete  revolution  and  then  overtake  the  earth 
before  it  comes  into  inferior  conjunction  again.  If  two 
persons  start  together  at  some  point  on  the  circumference 


ASTRONOMY.  47 

of  a  circle,  and  the  first  walks  faster  than  the  other,  he 
must  gain  the  whole  length  of  the  circumference  before 
he  comes  up  to  the-  second  again.  In  the  same  way, 
after  Venus  has  come  into  inferior  conjunction,  it  must 
gain  360°  upon  the  earth  before  it  can  come  into  inferior 
conjunction  again. 

=~L.  —  the  angular  space  passed  over  by  the  earth  in 

one  day.  ^-r-  —  angular  space  passed  over  by  Venus 
in  one  day. 

^-T-    —  ^—p-  •=.  the  angular  gain  of  Venus  upon  the  earth 
in  one  day.     But   Venus  gains  360°   in   S  days,   hence 
=  daily  gain  of  Venus. 

Hence  36°°        36°°  —  36°° 

JLJLCllV^C  ~ ~        — •    •  ~ — • 

'Divide  by  360,  and  we  have 

i  _    £  __  _£ 
/       P~~  S' 
PS—pS= 


. 

= 


46.  To  find  the  Sidereal  Period  of  a  Superior  Planet.  — 
The  sidereal  period  of  a  superior  planet  can  be  found  by 
a  similar  method.  In  this  case  the  earth  gains  upon 
the  planet. 

Let/  and  -S"  represent  the  sidereal  and  synodical  period 
of  a  superior  planet.  Then  ^  ---  ^-^-  =  daily  gain  of 
the  earth  upon  the  planet: 

360°  _  360°  _  360° 
P    '    '  S  ' 


48  ASTRONOMY. 

47.  Synodical  and  Sidereal  Periods  of  the  Planets.  —  The 
following  table  gives  the  synodical  and  sidereal  periods 
of  the  principal  planets  :  — 


Synodical  Period. 

Sidereal  Period. 

Mercury 

115.877  days 

87.969  days  or  3  months 

Venus 

583.921     « 

224.701       "        7!     " 

Earth 

365.256       "        i  year 

Mars 

779.936     « 

686.980       "        2  years 

Jupiter 

398.884     « 

4332.585       "      12     " 

Satlirn 

378.092     " 

10759.220       "      29     " 

Uranus 

369.656     " 

30686.821       "      84     " 

Neptune 

367.489     « 

60126.722       "    164     " 

SUMMARY. 

The  sidereal  period  of  the  earth  is  found  by  observing 
the  interval  between  two  successive  appearances  of  the 
sun  at  the  same  equinox,  or  two  successive  conjunctions 
of  the  sun  with  the  same  star.  (43.) 

An  inferior  planet  is  one  whose  orbit  lies  wholly  with- 
in the  earth's  orbit. 

A  superior  planet  is  one  whose  orbit  lies  wholly  with- 
out the  earth's  orbit. 

A  planet  is  in  inferior  conjunction  when  it  lies  in  the 
same  part  of  the  heavens  as  the  sun,  and  is  between  the 
earth  and  sun. 

A  planet  is  in  superior  conjunction  when  it  lies  in  the 
same  part  of  the  heavens  as  the  sun,  and  is  beyond  the 
sun. 

A  planet  is  in  opposition  when  it  lies  in  the  opposite 
part  of  the  heavens  from  the  sun. 

The  superior  planets  are  never  in  inferior  conjunction, 
and  the  inferior  planets  are  never  in  opposition. 

The  synodical  period  of  a  planet,  is  the  interval  between 


ASTRONOMY. 


49 


two  successive  oppositions  of  the  planet,  or  between  two 
successive  conjunctions  of  the  same  kind. 

The  synodical  period  is  ascertained  by  direct  observa- 
tion. (44.) 

The  sidereal  period  of  a  planet  is  the  time  it  takes  the 
planet  to  make  a  complete  revolution  about  the  sun. 

The  sidereal  period  of  a  planet  can  be  computed  when 
the  sidereal  period  of  the  earth  and  the  synodical  period 
of  the  planet  are  known.  (45,  46.) 


Fig.  17. 


HOW   TO    FIND   THE   DISTANCE   OF   THE 
PLANETS   FROM   THE   SUN. 

48.  To  find  the  relative  Distances  of  the  Inferior  Planets 
from  the  Sun.  —  We  have  now  seen  how  to  find  the  peri- 
odic times  of  the  planets,  which  must  have  been  known  to 
Kepler  before  he  could  discover  the  simple  relation  which 
the  periodic  times  of  the  planets  bear  to  their  mean  dis- 
tances from  the  sun.  We  must  next  see  how  we  can  find 
the  relative  distances  of  the  planets  from  the  sun.  We  will 
begin  with  the  inferior  planets. 

Let  ^  in  Figure  17,  represent  the 
position  of  Venus  at  its  greatest  elon- 
gation from  the  sun ;  S,  the  position  of 
the  sun ;  and  E  that  of  the  earth.  The 
line  E  Fwill  evidently  be  tangent  to  a 
circle  described  about  the  sun  with  a 
radius  equal  to  the  distance  of  Venus 
from  the  sun  at  the  time  of  this  great- 
est elongation.  Draw  the  radius  S  V 
and  the  line  S  E.  Since  S  V  is  a  ra- 
dius, the  angle  at  V  is  a  right  angle. 
The  angle  at  E  is  known  by  measure- 
ment, and  the  angle  at  S  =  90°  —  the 
angle  E.  In  the  right-angled  triangle 


50  ASTRONOMY. 

E  V S,  we  then  know  the  three  angles,  and  we  wish  to 
find  the  ratio  of  the  side  S  V  to  the  side  S  E. 

The  ratio  of  these  two  sides  may  be  found  by  construc- 
tion as  follows  :  — 

Draw  any  line,  as  A  B  (see  Figure  18),  and  from  the 
Fig  ig  point  A  draw  the  line  A  D 

at  right  angles  to   the  line 
A  B.     From   the   point   B 

G       draw  the  line  B  C,  making 

^""^JD       with  the  line  B  A  an  angle 
equal  to  the  angle  at  ,5  in 

Figure  17.  These  lines  will  intersect  at  some  point,  as 
E,  and  E  A  B  will  be  a  right-angled  triangle  similar  to 
E  V S,  and  the  side  A  B  will  have  the  same  ratio  to  BE 
as  V  S  has  to  S  E.  Measure  now  the  two  lines  A  B  and 
BE  by  means  of  the  scale  and  dividers,  and  the  ratio 
of  AB  to  BE,  and  consequently  of  V S  to  E  S,  be- 
comes known. 

The  ratio  of  these  lines  may  be  found  with  greater  ac- 
curacy by  trigonometrical  computation,  as  follows  :  — 


VS  \E  S  =  sin  SE  F:(sin  S  VE=  i).* 
Substitute  the  value  of  the  sine  of  £  E  V,  and  we  have 
VS-.E  £=.723  :  i. 

Hence  the  relative  distances  of  Venus  and  of  the  earth 
from  the  sun  are  .723  and  i. 

As  Venus  moves  in  an  ellipse,  and  its  greatest  elonga- 
tion takes  place  in  different  parts  of  its  orbit,  the  angle 
S  E  V  will  not  always  be  the  same.  In  order  to  get  the 
mean  distance  of  Venus  from  the  sun,  we  must  know  the 
average  value  of  its  greatest  elongation  from  the  sun. 
This  is  obtained  by  observing  a  large  number  of  such 
elongations. 

*  See  Appendix,  T.  i  and  3. 


ASTRONOMY. 


49.  To  find  the  relative  Distances  of  the  Superior  Plan- 
ets from  the  Sun.  —  Let  S,  e,  and  m,  in  Figure  19,  repre- 
sent the  relative  positions  of  the  sun,  the  earth,  and 


Fig.  19. 


Mars,  when  the  latter  planet  is  in  opposition.  Let  E 
and  M  represent  the  relative  positions  of  the  earth  and 
Mars  the  day  after  opposition.  At  the  first  observation 
Mars  will  be  seen  in  the  direction  e  m  A,  and  at  the 
second  observation,  in  the  direction  E  M  A. 

But  the  fixed  stars  are  so  distant  that,  if  a  line,  e  A, 
were  drawn  to  a  fixed  star  at  the  first  observation,  and  a 
line,  E  B^  drawn  from  the  earth  to  the  same  fixed  star 
at  the  second  observation,  these  two  lines  would  be  sen- 
sibly parallel ;  that  is,  the  fixed  star  would  be  seen  in 
the  direction  of  the  line  e  A  at  the  first  observation,  and 
in  the  direction  of  the  line  E  B,  parallel  to  e  A,  at  the 
second  observation.  But  if  Mars  were  seen  in  the  direc- 
tion of  the  fixed  star  at  the  first  observation,  it  would  ap- 
pear back,  or  west,  of  that  star  at  the  second  observation 
by  the  angular  distance  B  E  A  ;  that  is,  the  planet  would 
have  retrograded  that  angular  distance.  Now  this  retro- 
gression of  Mars  during  one  day  at  the  time  of  opposi- 
tion can  be  measured  directly  by  observation.  This 
measurement  gives  us  the  value  of  the  angle  B  E  A. 
But  we  know  the  rate  at  which  both  the  earth  and  Mars 
are  moving  in  their  orbits,  and  from  this  we  can  easily 


52  ASTRONOMY. 

find  the  angular  distance  passed  over  by  each  in  one 
day.  This  gives  us  the  angles  ESA  and  MSA.  We 
can  now  find  the  relative  length  of 'the  lines  MS  and 
E  S  (which  represent  the  distance  of  Mars  and  of  the 
earth  from  the  sun)  both  by  construction  and  by  trigono- 
metrical computation.  The  relative  length  of  these  lines 
can  be  found  by  construction,  as  follows.  Draw  any  line, 


Fig.  20. 


A  B,  then  through  the  point  A  draw  two  lines,  A  C  and 
A  D,  making  with  A  B  angles  respectively  equal  to  the 
angles  MSA  and  J5SA,  as  found  above.  Through 
any  point  on  the  line  A  D  draw  the  line  E  G,  parallel  to 
the  line  A  B  ;  and  draw  E  F>  making  with  E  G  an  angle 
equal  to  the  angle  B  E  A,  as  found  by  observation.  The 
triangle  A  E  F  will  evidently  be  similar  to  the  triangle 
E  S  M,  and  the  side  FA  will  bear  to  EA  the  same 
ratio  as  MS  bears  to  E  S.  This  ratio  can  be  found  by 
measurement  of  the  two  lines  A  F  and  A  E. 

This  ratio  can  be  determined  with  much  greater  accu- 
racy by  the  following  trigonometrical  calculation. 

Since  E  B  and  e  A  are  parallel,  the  angle  E  A  S  is 
equal  to  B  E  A. 

S  E  A  =  180°  •—  (E  S  A  +  E  A  S). 
ESM—ESA  —  MSA. 


We  have  then 

MS  :  E  S  =  sin  S  E  A  :  sin  E  MS. 


ASTRONOMY.  53 

Substituting  the  values  of  the  sines,  and  reducing  the 
ratio  to  its  lowest  terms,  we  have 

MS  :  E  S  =  1.524  :  i. 

Thus  we  find  that  the  relative  distances  of  Mars  and 
the  earth  from  the  sun  are  1.524  and  i.  By  the  simple 
observation  of  its  greatest  elongation  we  are  able  to  de- 
termine the  relative  distance  of  an  inferior  planet  and 
the  earth  from  the  sun ;  and  by  the  equally  simple  obser- 
vation of  the  daily  retrogression  of  a  superior  planet  we 
can  find  the  relative  distance  of  such  a  planet  and  the 
earth  from  the  sun. 

50.  The  Relative  Distances  of  the  Planets  from  the  Sun. 
—  In  this  way  the  relative  distances  of  the  principal  plan- 
ets have  been  found  to  be  as  follows  :  — 

Mercury  0-387 

Venus  0.723 

Earth  i.oo 

Mars  1-524 

Jupiter  5-2°3 

Saturn  9.539 

Uranus'  19-183 

Neptune  30.037 

Knowing  the  periodic  times  of  the  planets  and  their 
relative  distances  from  the  sun,  Kepler  found  the  ratio 
which  these  bear  to  each  other  by  the  method  of  trial 
and  error,  which  he  had  previously  used  in  ascertaining 
the  form  of  the  orbits  of  the  planets. 

51.  To  find  the  Distance  of  the  Earth  from  the  Sun.  — 
We   have    now   found   the    relative    distances    of   all   the 
planets,  including  the   earth,   from   the   sun.     If  now  we 
can  find  the  distance  of  the  earth  from  the  sun  in  miles,  • 
we  can  easily  find  the  distances  of  all  the  planets  from 
the  sun  in  miles. 

Now  it  is  evident  that,  when  two  straight  lines   cross 
5* 


54 


ASTRONOMY. 


each  other,  the  distances  between  these  two  lines  at  any 
two  points  are  proportionate  to  the  distance  of  these 
points  from  the  intersection  of  the  two  lines. 

Thus,  suppose   the   two   straight   lines   A  B   and    CD 
(Figure  21)  cross  each  other  at  £,  and  suppose  the  point 


Fig.  21. 


G  be  twice  as  far  from  E  as  F  is  from  the  same  point ; 
the  distance  between  the  two  lines  will  be  twice  as  great 
at  G  as  at  F. 

Now  it  occasionally  happens  that  Venus,  at  inferior 
conjunction,  passes  directly  across  the  disc  of  the  sun. 

In  Figure  22  let  V  represent  the  position  of  Venus  at 


Fig.  22. 


inferior  conjunction,  A  B  the  position  of  the  earth,  and 
CD  that  of  the  sun. 

An  observer  at  A  would  see  Venus  crossing  the  sun  in 
the  line  CD,  and  an  observer  at  B  would  see  it  cross 
the  sun  in  the  line  E  F.  These  two  chords  will  be  par- 
allel to  each  other,  and  the  distance  between  them  will 


ASTRONOMY. 


55 


be  equal  to  the  distance  between  the  two  lines  A  H  and 
B  G  at  the  distance  If  from  their  intersection  at  V.  This 
distance  bears  to  the  distance  between  the  two  lines  at 
A  the  same  ratio  that  the  distance  V  H  bears  to  the 
distance  V  A. 

But  we  have  already  found  that  the  distance  AH  bears 
to  the  distance  V  H  the  ratio  of  i  to  .723.  But  V  A  = 
A  H—  V H.  Hence  VA  bears  to  VH  the  ratio  277 
to  723.  Then  G  H  \  A  B  =  723  :  277. 

Hence,  if  we  know  the  distance  between  the  two  ob- 
servers at  A  and  B  in  a  straight  line  in  miles,  we  can 
find  the  distance  G  H  in  miles. 

Since  Venus  revolves  about  the  sun  from  west  to  east, 
it  will  appear  to  us  to  be  moving  westward  when  it 
crosses  the  sun,  while  the  sun  is  apparently  moving  east- 
ward. We  however  know  the  rate  at  which  both  the 
sun  and  Venus  are  moving.  Hence,  if  we  know  the  time 
that  it  takes  Venus  to  cross  the  sun's  disc,  we  can  find 
what  angular  distance  both  have  passed  over  in  this  time. 
And  as  they  are  moving  in  opposite  directions,  the  sum 
of  these  distances  will  give  the  angular  measure  of  the 
chord  described  by  Venus  across  the  sun's  disc. 

Each  observer,  then,  thus  notices  carefully  the  time 
that  it  takes  Venus  to  cross  the  sun's  disc.  From  this 
observed  time  each  is  able  to  find  the  angular  value  of 
the  chord  described  by  the  planet. 

Let  A  B  and  CD  (Figure  23) 
represent  the  chords  described  on 
the  sun's  disc  by  the  passage  of 
Venus.  Draw  the  radii  E  F,  E  B, 
and  E  D.  The  radius  E  F  is 
drawn  perpendicular  to  the  two 
chords,  and  therefore  bisects  them. 
The  angular  diameter  of  the  sun 
can  be  found  directly  by  observa- 


Fig.  23. 


56  ASTRONOMY. 

tion.  Hence  the  angular  value  of  each  of  the  radii  E  B 
and  E  D  is  known  ;  also  the  angular  values  of  G  B  and 
H  D,  the  halves  of  A  B  and  CD..  Hence  in  each  of 
the  right-angled  triangles  E  G  B  and  E  H  D  the  angu- 
lar values  of  the  hypothenuse  and  of  one  side  are  known, 
and  the*  angular  value  of  the  other  side  can  be  easily 


found.       For  ^~B*  —  £^2  =  ~G£2  •  and  £~D2  —  JT& 
~         But  G  H=  G  E  —  HE. 


The  angular  value  of  G  If  is  then  known,  and  also  its 
linear  value.  Dividing  the  linear  value  by  the  number 
of  seconds  in  its  angular  value,  we  find  how  long  a  line 
will  subtend  an  angle  of  i"  at  the  distance  of  the  sun. 
Knowing  this,  we  know  how  large  an  angle  will  be  sub- 
tended by  the  earth's  radius  at  the  distance  of  the  sun. 

In  Figure  24,  let  S 

Flg-24"  represent  the  place 

of  the  sun,  and  C 
the  centre  of  the 
earth.  Draw  the 
line  S  A  tangent 
to  the  surface  of 
the  earth,  and  draw 
the  radius  A  C.  The  triangle  SAC  will  be  right- 
angled  at  A.  The  comparative  length  of  the  lines  A  C 
and  C  S  can  now  be  determined  either  by  construction, 
as  in  section  45,  or  by  the  following  computation  :  — 

C  S  :  C  A  =  i  :  sin  C  S  A. 
Substituting  the  value  of  sin  C  S  A,  we  find 

C  S  :  C  A  =  23,750  (in  round  numbers)  :  i. 

Hence  the  distance  of  the  sun  from  the  earth  is,  in 
round  numbers,  23,750  times  the  length  of  the  earth's 
radius  in  miles. 

Now  if  we  can  find  the  length  of  the  earth's  radius  in 


ASTRONOMY.  57 

miles,  and  the  distance  in  a  straight  line  between  the 
points  A  and  B  (Figure  22),  we  can  find  the  distance  of 
the  earth  and  of  each  of  the  planets  from  the  sun  in 
miles. 

52.  To  find  the  Length  of  the  Radius  of  the  Earth  in 
Miles.  —  We  know  that  the  circumference  of  a  .circle  is 
3.1416  times  as  long  as  its  diameter.     Now,  if  the  earth 
is  an  exact  sphere,  every  meridian  of  the  earth  will  evi- 
dently be  an  exact  circle ;    and  if  we  can  measure  any 
known  fraction  of  one  of  these  meridians,  we  can  easily 
find  its  whole  length  ;   and  from  this   the  length  of  the 
diameter  of  the  earth,  which  is  of  course  the  diameter  of 
every  great  circle  of  the  earth. 

53.  How  to  measure  a  known  Fraction  of  a  Meridian. — 
Suppose   two   places,  A  and  B  (Figure   25),  to  be  situ- 

Fig.  25. 


ated,  the  one,  for  instance,  at  Shanklin  Down,  in  the 
Isle  of  Wight,  and  the  other  on  the  little  island  of  Balta, 
in  the  Shetland  Isles.  We  wish  to  know,  first,  what 
fraction  of  a  whole  meridian  is  the  arc  included  between 
these  two  places ;  and  second,  how  long  this  arc  is  in 
miles. 

Any  line  which  is  perpendicular  to  a  tangent  to  a 
circle  at  the  point  of  contact  is  said  to  be  vertical  to 
the  circle ;  and,  if  two  verticals  be  prolonged  within  the 
circumference  of  the  circle,  they  will  meet  at  the  centre 
of  the  circle.  The  fraction  of  the  circumference  included 
between  the  two  verticals  depends  upon  their  inclination 
to  each  other.  If  they  are  inclined  to  each  other  at  an 


ASTRONOMY. 


angle  of  i°,  the  arc  included  between  them  is  ^^  of  the 
whole  circumference,  and,  if  they  are  inclined  to  each 
other  at  an  angle  of  12°,  the  arc  included  between  them 
is  -3*3-  of  the  whole  circumference. 

But  a  plumb-line  is  always  vertical  to  a  great  circle 
of  the  earth ;  hence,  if  we  can  find  the  inclination  of  a 
plumb  line  at  A  to  one  at  B,  we  know  what  fraction  of 
the  whole  meridian  the  arc  included  between  A  and  B 
is.  The  angle  which  the  directions  of  the  plumb-lines 
at  the  two  stations  make  with  each  other  can  be  ascer- 
tained by  means  of  the  Zenith  Sector. 

This  instrument  is  shown  in  Figure  26.     It  consists  of 
a    telescope    swinging   upon    pivots    A  B, 
Fig.  26.  an(j  having   attached  to  it  an  arc  CD  £, 

graduated  into  degrees  and  minutes.  There 
is  a  plumb-line,  B  F,  connected  with  the 
upper  end  of  the  telescope,  or  with  one  of 
the  pivots.  This  plumb-line  is  a  very  fine 
silver  wire  supporting  a  weight,  and  kept' 
steady  by  hanging  in  water.  It  gives  us 
the  direction  of  the  vertical. 

The  zenith  sector  is  taken  to  one  of 
the  stations,  and  the  telescope  directed 
to  a  bright  star  upon  the  meridian  near 
the  zenith.  The  number  of  degrees  and 
minutes  which  the  plumb-line  hangs  from 
the  zero  point  at  the  centre  of  the  telescope  on  the  grad- 
uated arc  is  observed.  The  sector  is  now  taken  to  the 
other  station,  and  the  same  star  is  again  observed  when 
upon  the  meridian,  and  the  number  of  degrees  and  min- 
utes that  the  plumb-line  hangs  from  the  zero  point  on 
the  arc  is  again  observed.  Now,  since  the  directions  of 
the  telescope  at  the  two  stations  are  sensibly  parallel, 
the  difference  of  the  degrees  and  minutes  that  the  plumb- 
line  at  the  two  stations  hangs  away  from  the  telescope 


ASTRONOMY.  59 

must  be  the  amount  by  which  the  verticals  at  the  two 
places  are  inclined  .to  each  other.  Suppose  that  this  dif- 
ference amounts  to  12°,  then  the  arc  A  B  is  equal  to  -fa 
of  the  whole  circumference  of  the  meridian. 

As  these  two  stations  are  700  or  800  miles  apart,  we 
cannot  of  course  measure  the  distance  between  them  by 
using  only  a  yard-stick,  though  the  distance  between 
these  stations  must  be  calculated  by  means  of  a  distance 
first  measured  by  a  yard-stick. 

54.  Triangulation.  —  Such    measurements    are    effected 
by  means  of  a  system  of  triangulation.     Suppose  that  we 
have   three   places,   £,  F,   and  G  (Figure   27);  the   two 
nearest,  E  and  F,  on  a  plain, 

and  perhaps  six  or  eight  miles 
apart ;  a  third,  G,  at  a  consid- 
erable distance,  perhaps  inac- 
cessible from  E  and  F,  at  least 
in  a  straight  line.  The  dis- 
tance of  G  from  either  E  or  F,  which  cannot  well  be 
measured,  can  be  readily  found  by  measuring  the  line 
F  Fj  and  the  angle  which  this  line  makes  with  lines 
drawn  from  E  and  F  to  the  point  G.  For  we  may  draw 
any  line,  E  F,  and  from  its  extremities  draw  the  lines 
E  G  and  F  G,  making  with  the  first  line  the  angle  de- 
termined by  measurement,  and  by  means  of  the  scale 
and  dividers  the  lines  F  G  and  F  G  can  be  measured. 
We  can  also  find  the  length  of  the  line  by  trigonometri- 
cal computation.* 

55.  The  Measurement  of  a  Base  Line.  —  For  every  system 
of  triangulation  one  line  must  be  measured.     This  line  is 
called  a  base  line.     In  extensive  systems  of  triangulation, 
where  great  accuracy  is  required,  the  measurement  of  the 
base  line  is  a  very  troublesome  operation.     It  seems  at 
first   thought  extremely  easy  to  measure  a  straight   line, 

*  See  Appendix,  I.  5. 


60  ASTRONOMY. 

but,  in  fact,  there  is  nothing  more  difficult.  In  the  first 
place  what  are  we  to  measure  it  with?  If  we  use  bars 
of  metal,  they,  as  we  have  seen,  expand  when  warmed 
and  contract  when  cooled,  and  consequently  are  not  al- 
ways of  the  same  length.  The  line  must  be  measured 
by  the  yard.  But  the  yard  is  a  certain  definite  length, 
and  cannot  therefore  be  the  length  of  any  rod  whose 
length  changes  with  the  temperature  to  which  it  is  ex- 
p3sed.  A  rod  can  be  a  yard  long  only  at  a  particular 
temperature.  Many  base  lines  have  been  measured  with 
rods  and  chains  of  iron  or  brass,  but  every  precaution 
has  been  used  in  every  part  of  the  operation  to  screen 
them  from  changes  of  temperature,  by  covering  them 
with  tents ;  putting  perhaps  half  a  dozen  bars  at  a  time 
in  a  row,  with  several  thicknesses  of  tent  over  them,  so 
as  to  protect  them  effectually  from  the  sun  and  wind. 
Having  taken  this  precaution  to  shield  them  from  the 
effects  of  changes  of  temperature,  thermometers  are  placed 
by  the  side  of  the  bars,  and  their  temperature  thus  as- 
certained. Knowing,  then,  their  length  at  a  given  tem- 
perature, and  how  much  they  expand  for  a  given  rise  of 
temperature  or  contract  for  a  given  fall  of  temperature, 
the  length  represented  by  the  bars  when  used  can  be 
ascertained.  Figure  28  represents  another  contrivance 

which     has     been 
used     with     great 

JE?     success.       It    con- 

"""VJA""" '"' KZB^F 

^m^^^^^^^^^m^^f^  sists  of  a  combina- 
tion of  two  bars  ; 

one,  A  B  C,  of  brass,  and  the  other,  D  E  F,  of  iron. 
These  bars  are  connected  at  the  middle,  E  B,  and  they 
have  projecting  tongues,  ADG  and  C F H.  These 
tongues  turn  easily  on  pivots  at  A,  D,  C,  and  F.  The 
length  G  D,  is  just  |  of  G  A,  and  H  F  just  %  of  If  C. 
Now  brass  expands  more  than  iron  for  the  same  rise  of 


ASTRONOMY.  6 1 

temperature.  Suppose  the  rod  A  B  C  to  remain  of  the 
same  length,  and  the  rod  D  E  F  to  expand  ;  the  points 
G  and  H  would  evidently  be  carried  farther  apart.  But 
suppose  the  rod  D  E  F  to  remain  of  the  same  length, 
and  the  rod  A  B  C  to  expand ;  the  points  G  and  .//"will 
come  nearer  together.  Suppose  now  that  both  rods  ex- 
pand together,  but  that  the  rod  ABC  expands  just  as 
much  more  rapidly  than  the  other  rod  as  the  distance 
A  G  is  greater  than  the  distance  D  G ;  the  points  .//and 
G  will  evidently  remain  at  the  same  distance  from  each 
other.  Now  we  know  that  brass  expands  if  times  as 
fast  as  iron,  and  the  distance  A  G  is  i§  times  the  dis- 
tance D  G. 

A  number  of  combined  bars  like  these  are  placed  one 
after  another,  with  a  small  interval  between  each  two ; 
and  then  the  question  is,  how  is  the  interval  between 
them  to  be  measured  ?  It  will  not  do  to  make  one  bar 
touch  the  other,  because  expansions  may  be  going  on  in 
one  of  the  series  of  bars,  and  it  would  jostle  the  others 
throughout  the  whole  extent.  This  small  distance  is 
sometimes  measured  by  means  of  microscopes  mounted 
on  the  same  principle  as  the  bars,  so  that  the  measure 
which  they  give  is  not  affected  by  temperature.  In  some 
cases,  glass  wedges  have  been  dropped  between  the  suc- 
cessive bars,  in  others  sliding  tongues  have  been  used. 
The  result  of  all  this  has  been,  that  a  distance  of  eight 
or  ten  miles  has  been  measured  to  within  a  very  small 
fraction  of  an  inch. 

We  have  been  thus  minute  in  our  account  of  the  meas- 
urement of  a  base  line,  to  give  an  illustration  of  the  ex- 
treme care  that  must  be  taken  in  measuring  lines  and 
angles  which  are  to  be  used  in  the  computation  of 
celestial  distances.  And  we  see  the  necessity  of  this 
great  carefulness  when  we  remember  that  this  base  line, 
which  does  not  exceed  eight  or  ten  miles,  is  to  be  used, 
6 


62 


ASTRONOMY. 


Fig.  29. 


first,  in  the  computation  of  the  radius  of  the  earth,  which 
is  some  4,000  miles  long ;  then  in  computing  the  distance 
of  the  sun,  which  is  some  24,000  times  the  length  of  the 
earth's  radius ;  then  also  in  computing  the  distance  of 
Neptune  from  the  sun,  which  is  some  thirty  times  the 
distance  of  the  earth  from  the  sun  ;  and  finally,  as  we 
shall  see,  in  computing  the  distance  of  the  fixed  stars, 
which  are  thousands  of  times  more  remote  than  Neptune 
from  the  sun.  It  is  like  measur- 
ing a  length  of  a  hundredth  of  an 
inch  on  the  wall  in  hair-breadths  as 
a  basis  for  computing  the  dimen- 
sions of  a  house  in  hair-breadths. 
A  slight  mistake  in  the  measure 
of  the  first  length  would  lead  to 
an  enormous  error  in  the  final 
result. 

56.  But  the  point  B  (Figure  25) 
is  too  distant  to  be  seen  from  the 
extremities  of  our  base  line,  one 
end  of  which  may  be  at  A.  We 
must,  therefore,  approach  it  step 
by  step  with  our  triangles. 

The  method  by  which  this  is 
accomplished,  and  the  distance 
between  the  points  finally  deter- 
mined, is  illustrated  by  Figure  29. 
Suppose  we  are  to  find  the  dis- 
tance between  the  points  A  and 
B.  First  measure  the  base  line 
AC.  The  angle  which  this  line 
makes  with  a  north  and  south  line 
is  then  ascertained.  To  do  this,  a 
transit  instrument  is  set  up  at  A, 
and  its  telescope  so  adjusted  that 


ASTRONOMY.  63 

it  will  point  exactly  to  the  north  celestial  pole.  It  is 
then  turned  down  Jo  the  horizon,  and  a  mark  is  set  up 
at  a  distance  in  the  direction  of  the  north  as  thus  found. 
A  theodolite  is  then  set  up  at  A.  This  instrument  consists 
of  a  telescope  attached  to  a  graduated  circle  which  is  ar- 
ranged so  as  to  turn  horizontally.  When,  therefore,  the 
telescope  of  the  instrument  is  turned  horizontally,  the 
graduate:!  circle  carried  around  with  it  shows  how  many 
degrees  it  has  been  turned.  The  telescope  is  first  di- 
rected to  the  mark,  and  then  turned  around  till  it  points 
to  the  station  C.  The  number  of  degrees  that  the  tele- 
scope has  been  turned,  as  indicated  by  the  graduated 
circle,  shows  the  angle  which  the  line  A  C  makes  with 
the  north  and  south  line.  A  third  station,  D,  is  then 
chosen,  which  can  be  distinctly  seen  from  both  A  and  C, 
and  a  signal  erected  at  this  point.  The  telescope  of  the 
theodolite  is  again  turned  to  C  and  then  to  D,  and  the 
number  of  degrees  that  the  telescope  is  turned  in  passing 
from  C  to  D  gives  the  angle  CAD.  The  line  A  D  is 
then  drawn  so  as  to  make  this  angle  with  A  C.  The  the- 
odolite is  next  carried  to  C  and  pointed  to  A,  and  then 
turned  till  it  points  to  D.  The  number  of  degrees  it  has 
to  be  turned  gives  the  angle  D  C  A.  The  line  D  C  is 
then  drawn,  making  this  angle  with  C  A. 

A  fourth  station,  E,  is  now  selected,  which  can  be 
readily  seen  at  C  and  D.  Then  E  C  D  and  E  D  C  are 
measured  by  means  of  the  theodolite,  as  before,  and  the 
lines  C  E  and  D  E  are  drawn,  making  die  angles  at  C 
and  D  equal  to  those  measured.  Thus  we  go  on  step 
by  step,  measuring  the  angles  and  drawing  the  triangles, 
till  we  reach  the  point  B.  The  distance  B  A  can  then 
be  measured  by  means  of  the  scale  and  dividers,  and 
compared  with  the  length  of  the  base  line  A  C.  The 
distance  of  the  stations  D,  E,  F,  etc.  from  the  preceding 
station,  and  the  distance  of  B  from  A,  can  be  more  accu- 


64  ASTRONOMY. 

rately  determined  by  trigonometrical  computation.  In 
the  first  triangle,  the  side  C  A  and  1^ie  angles  at  C  and 
A  are  known  by  measurement  ;  hence  the  other  parts  of 
the  triangle  can  be  readily  computed.  Then,  in  the  sec- 
ond triangle,  the  side  CD  and  the  angles  at  C  and  D 
become  known,  and  the  other  part  of  this  triangle  can 
be  computed  ;  and  so  on  to  the  end.  Then,  by  drawing 
the  dotted  lines,  a  series  of  right-angled  triangles  is 
formed,  in  each  of  which  the  hypothenuse  is  known,  and 
one  of  the  acute  angles  can  be  readily  found.  For  in 
the  right-angled  triangle  A  N  D  the  angle  N  A  D  •=. 
D  A  C  —  N  A  C.  In  the  right-angled  triangle  F  M  D, 


This  may  be  shown  by  drawing  a  line  through  D  par- 
allel to  N  S.  The  sum  of  all  the  angles  at  the  point  D 
will  then  be  180°.  But  the  angle  formed  by  FD  with 
the  line  supposed  to  be  drawn  will  be  equal  to  MFD, 
and  the  angle  formed  by  A  D  with  the  same  line  will  be 
equal  to  D  A  N.  In  a  similar  manner  the  angles  F  H  L 
and  H  B  K  can  be  found.  Hence  the  parts  of  these 
right-angled  triangles  can  be  computed,  and  the  lengths 
of  the  sides  AN,  M  F,  L  K,  and  KB  can  be  found. 
But  the  sum  of  these  sides  is  evidently  equal  to^the 
length  of  the  line  A  B. 

57.  In  this  way  it  has  been  ascertained,  that,  if  the 
two  plumb-lines  at  A  and  B  (Figure  25)  are  inclined  to 
each  other  at  an  angle  of  12°,  the  length  of  the  arc  be- 
tween them  in  miles  is  about  830  miles.  From  this  we 
conclude  that  we  must  pass  over  an  arc  69^  miles  long 
in  order  to  find  the  distance  of  two  places  whose  verti- 
cals are  inclined  one  degree. 

69^  X  360,  then,  gives  the  circumference  of  the  earth, 
and  this  divided  by  3.1416  gives  the  diameter  of  the  earth, 
one  half  of  which  is  the  radius,  which  is  thus  found  to 
be  about  4,000  miles  long. 


ASTRONOMY.  65 

58.  The  Earth  not  a  perfect  Sphere.     By  measuring  arcs 
of  meridian  in  different  parts  of  the  earth,  we  find  that 
the  arcs  included  between  two  places  whose  verticals  are 
inclined  to  each  other  one  degree  are  not  always  of  the 
same  length  in  miles.     It  has  been  found  that  towards 
the  poles  two  places  must  be  farther  apart  than  near  the 
equator,  to  have  their  verticals  inclined  to  each  other  one 
degree.      The   earth,  then,  cannot   be   an   exact   sphere. 
Since  the  arc  between  two  places  whose  verticals  are  in- 
clined one  degree  is  longer  near  the  poles  than  at  the 
equator,  the  curvature  of  the  earth  at  the  poles  must  be 
that  of  a  larger  circle  than  the  curvature  at  the  equator, 
and  since   the  larger  the  circle  the  less   rapidly  does  it 
curve,  we  see  that  the  earth   is  slightly  flattened  at  the 
poles.     The  polar  diameter  of  the  earth  has  been  found 
to  bear  to  the  equatorial  the  ratio  of  299  to  300. 

59.  Knowing   the   exact   size   and   form   of  the   earth, 
the  distance  between  the  two  stations  A  and  B  (Figure 
22)  in  a  straight  line  can  be  computed. 

The  transits  of  Venus,  by  which  the  sun's  distance 
from  the  earth  can  be  determined,  occur  in  pairs  at  in- 
tervals of  eight  years  separated  by  more  than  one  hun- 
dred years.  The  last  pair  occurred  in  1761  and  1769, 
and  the  next  will  be  in  1874  and  1882. 

It  is  now  supposed  by  many  that  there  was  an  error 
in  one  of  the  observations  of  the  last  transit  of  Venus, 
so  that  the  distance  of  the  sun  as  computed  from  these 
observations  is  some  3,000,000  of  miles  'greater  than  it 
really  is.  Hence  the  next  transits  of  Venus  are  looked 
forward  to  with  great  interest. 

60.  The  Mean  Distances  of  the  Planets.  —  The  follow- 
ing is  a  table  of  the  mean  distances  of  the  most  impor- 
tant  planets   from   the   sun,  as   computed  from   the  last 
transit  of  Venus  :  — 

6* 


66  ASTRONOMY. 

Mercury  37,000,000  miles 

Venus  69,000,000  " 

Earth  95,000,000  " 

Mars  145,000,000  " 

Jupiter  436,000,000  " 

Saturn  909,000,000  " 

Uranus  1,828,000,000  " 

Neptune  2,862,000,000  " 

SUMMARY. 

The  distance  of  a  planet  from  the  sun  compared  with 
the  earth's  distance  from  the  same  is  called  its  relative  dis- 
tance from  the  sun. 

To  find  the  relative  distance  of  an  inferior  planet  from 
the  sun,  its  greatest  elongation  must  be  measured ;  and  the 
right-angled  triangle  which  the  earth,  the  planet,  and  the 
sun  then  form  must  be  computed.  (48.) 

To  find  the  relative  distance  of  a  superior  planet  from 
the  sun,  the  retrogression  of  the  planet  during  one  day, 
when  it  is  in  opposition,  must  be  measured  ;  and  the  tri- 
angle which  the  earth,  the  planet,  and  the  sun  then  form 
must  be  computed.  (49.) 

The  distance  of  the  earth  from  the  sun  is  found  by 
means  of  the  transits  of  Venus. 

To  find  this  distance,  we  must  determine  the  angle  sub- 
tended by  the  diameter  of  the  sun,  and  by  two  chords 
which  Venus,  as  seen  by  two  observers,  one  north  and  the 
other  south  of  the  equator,  describes  across  the  sun's  disc  ; 
the  relative  distance  of  Venus  and  of  the  earth  from  the 
sun  ;  and  the  size  and  shape  of  the  earth. 

The  angle  subtended  by  the  diameter  of  the  sun  is 
ascertained  by  direct  measurement. 

The  angle  subtended  by  the  chords  described  by  Venus 

is  ascertained  by  observing  the  transit  of  Venus.     (51.) 

i 


ASTRONOMY.  67 

The  size  and  shape-  of  the  earth  are  found  by  meas- 
uring known  arcs  of  meridians  on  different  parts  of  the 
earth.  (53-56.) 

The  actual  distance  of  any  planet  from  the  sun  can  be 
found  by  multiplying  its  relative  distance  by  the  distance 
of  the  earth  from  the  sun. 

HOW  TO  FIND  THE  DISTANCE  OF  THE  MOON. 

6 1.  We  have  already  ascertained  the  actual  distance 
of  the  earth,  as  well  as  of  all  the  other  planets,  from 
the  sun,  but  as  yet  we  do  not  know  the  distance  of  the 
moon  from  the  earth.  We  have  also  seen  that  all  the 
planets,  though  they  appear  to  revolve  about  the  earth, 
really  revolve  about  the  sun,  but  the  moon's  motion 
among  the  stars  can  be  explained  only  on  the  supposition 
that  she  revolves  about  the  earth. 

The  ancients  ascertained  the  distance  of  the  moon  with 
considerable  accuracy  by  the  observation  of  her  eclipses. 
They  knew  that  these  phenomena  were  caused  by  the 
passage  of  the  moon  through  the  earth's  shadow.  Now 
the  earth's  shadow  is  not  very  much  narrower  at  the  dis- 
tance of  the  moon  than  at  the  surface  of  the  earth,  and 
the  average  length  of  time  the  moon  takes  to  pass  through 
that  shadow  is  about  four  hours.  The  moon  passes 
over  a  part  of  her  orbit  equal  to  the  diameter  of  the 
earth  in  about  four  hours,  and  consequently  she  passes 
over  a  length  of  her  orbit  equal  to  six  diameters  of  the 
earth  in  a  day,  and,  as  she  completes  a  revolution  in 
about  thirty  days,  her  whole  orbit  must  be  about  one 
hundred  and  eighty  times  as  long  as  the  diameter  of  the 
earth.  Consequently  the  diameter  of  the  moon's  orbit 
is  about  sixty  times  the  diameter  of  the  earth,  and  the 
distance  of  the  moon  about  thirty  times  the  diameter  of 
the  earth. 


68 


ASTRONOMY. 


62.  Parallax.  —  The  distance  of  the  moon  can  now 
be  measured  by  means  si  parallax. 

The  following  illustration  shows  that  this  is  really  the 
method  by  which  we  commonly  estimate  distance.  If 
you  place  your  head  in  a  corner  of  a  room  or  against  a 
high-backed  chair,  and  close  one  eye,  and  allow  another 
person  to  put  a  lighted  candle  on  a  table  before  you, 
and  if  you  then  try  to  snuff  the  candle,  with  one  eye  still 
shut,  you  will  find  that  you  cannot  do  it :  you  will  prob- 
ably fail  nine  times  out  of  ten.  But  if  you  open  the 
other  eye,  the  charm  is  broken  ;  or  if,  without  opening 
the  other  eye,  you  move  your  head  sensibly,  you  are 
enabled  to  judge  of  the  distance. 

In  Figure  30  let  A  and  B  be  the  two  eyes,  and  C  an 
object  which  is  first  viewed  with  the  eye  A  alone.  This 

Fig.  30. 


eye  alone  has  no  means  of  judging  of  the  distance  of  C. 
All  that  it  can  tell  is  that  this  object  is  in  the  direction 
of  A  C,  but  there  is  nothing  by  which  it  can  judge  of 
its  distance  in  that  line.  Suppose  now  the  other  eye,  £, 
is  opened  and  turned  to  C,  then  there  is  a  circumstance 
introduced  which  is  affected  by  the  distance,  namely,  the 
difference  of  direction  of  the  two  eyes.  While  the  object 
is  at  C,  the  two  eyes  are  turned  inward  but  very  little  to 
see  it ;  but  if  the  object  is  brought  quite  close,  .as  at  Z>, 


ASTRONOMY.  69 

then  the  two  eyes  have  to  be  turned  inward  considerably 
to  see  it ;  and  from  this  effort  of  turning  the  eyes  we 
acquire  some  notion  of  the  distance.  We  cannot  lay 
down  any  accurate  rule  for  the  estimation  of  the  distance ; 
but  we  see  clearly  enough  in  this  explanation,  and  we 
feel  distinctly  enough  when  we  make  the  experiment,  that 
the  estimation  of  distance  does  depend  upon  this  differ- 
ence of  direction  of  the  eyes.  Now,  this  difference  of 
direction  of  the  two  eyes  is  a  veritable  parallax ;  and  this 
is  what  we  mean  by  parallax,  that  it  is  the  difference  of 
direction  of  an  object  as  seen  in  two  different  places. 
The  two  places  in  the  above  experiment  are  the  two 
eyes  in  the  head.  The  distance  of  the  moon  is  found  by 
precisely  the  same  method.  The  two  eyes  in  the  head 
will  be  two  telescopes,  one  in  the  observatory  at  Green- 
wich, and  the  other  in  the  observatory  at  the  Cape  of 
Good  Hope ;  and  the  difference  of  direction  of  the  eyes 
becomes  the  difference  of  direction  of  these  two  tele- 
scopes when  ppinted  at  the  moon.  When  this  difference 
of  direction  becomes  known  the  distance  of  the  moon  is 
easily  computed. 

63.  How  to  find  the  Difference  of  the  Direction  of  the 
two  Telescopes  when  turned  to  the  Moon.  —  The  difference 
of  direction  of  the  two  telescopes  when  pointed  at  the 
moon  is  found  by  means  of  the  mural  circle.  By  means 
of  this  the  zenith  distances  of  the  north  celestial  pole 
and  of  the  moon  are  observed  at  Greenwich,  and  the  sum 
of  these  distances  gives  the  north  polar  'distance  of  the 
moon  as  seen  at  Greenwich. 

By  means  of  this  same  instrument  the  zenith  distances 
of  the  south  celestial  pole  and  of  the  moon  are  also 
observed  at  the  Cape  of  Good  Hope  at  the  same  time 
that  the  observations  were  made  at  Greenwich.  The 
sum  of  these  zenith  distances  gives  the  south  polar  dis- 
tance of  the  moon.  It  is  found,  for  instance,  that  the 


ASTRONOMY. 


north  polar  distance  of  the  moon  as  obtained  at  Green- 
wich is  1  08°,  and  that  the  south  polar  distance  as  ob- 
served at  the  Cape  of  Good  Hope  is  73^°.  The  sum  of 
these  two  polar  distances  is  then  i8i|°. 

Suppose  now  that  G  and  C  in  Figure  31  represent  the 
position  of  the   observatories  at   Greenwich   and   at   the 


Fig.  31 


Cape  of  Good  Hope,  and  that  G  P  and  C  P1  represent 
the  direction  of  the  north  and  south  poles  of  the  heavens 
respectively  from  each  of  these  stations.  The  line  G  P 
has  of  course  a  direction  just  opposite  to  that  of  the  line 
C  P'.  The  line  G  M  represents  the  direction  of  the  tele- 
scope at  Greenwich  when  turned  toward  the  moon,  and 
the  line  C  M  represents  the  direction  of  the  telescope  at 
the  Cape  of  Good  Hope  when  turned  toward  the  moon. 
Suppose  now  that  the  telescope  at  each  observatory  be 
turned  toward  the  same  fixed  star.  G  S  will  be  the  di- 
rection of  the  telescope  at  Greenwich,  and  C  S'  the  di- 
rection of  the  telescope  at  the  Cape  of  Good  Hope. 
Now  when  the  north  polar  distance  of  any  fixed  star  is 
measured  at  Greenwich,  and  the  south  polar  distance  of 
the  same  star  is  measured  at  the  Cape  of  Good  Hope, 


ASTRONOMY.  7 1 

the  sum  of  these  polar  distances  always  equals  180°;  that 
is,  the  angle  S  G  P  +  S  C  P'  =  180°.  Hence  S  G 
and  S  C  must  be  parallel.  For  S  G  P  +  S  G  P'  = 
180°.  Therefore  S'  CP'  —  SGP' ;  that  is,  S  G  and  S*  C 
are  parallel. 

We  have  found  that  M  G  P  +  M  C  P'  =  i8ij.  The 
two  lines  M  G  and  J/  C  must  then  be  inclined  to  each 
other  at  an  angle  of  ij°,  for  if  these  two  lines  were  par- 
allel the  two  angles  M  G  P  +  M  C  P'  would  be  equal 
to  1 80°. 

We  have  now  found  the  difference  of  direction  of  the 
two  telescopes  when  turned  toward  the  moon.  Now 
since  the  exact  size  and  form  of  the  earth  are  known, 
the  length  of  the  line  G  C  and  the  angle  M  G  C  can  be 
computed,  and  the  distance  M  G  can  then  be  found  by 
construction  or  by  computation. 

64.  The  Moon's  Parallax.  —  This  gives  the  distance  of 
the  moon  from  each  of  the  observatories  G  and  C.  It 
is  convenient,  however,  to  make  all  our  calculations  of 
the  moon's  place  with  reference  to  the  centre  of  the  earth. 
By  reference  to  the  above  figure  it  will  be  seen  that  the 
direction  of  the  moon  is  not  the  same  when  seen  from 
the  centre  of  the  earth  E  as  when  seen  from  its  surface 
at  G  or  C.  The  difference  of  the  directions  of  the  moon 
as  seen  at  Greenwich  and  as  seen  from  the  centre  of  the 
earth  is  called  the  moon's  parallax  at  Greenwich.  Thus 
the  angle  G  ME  is  the  moon's  parallax  at  Greenwich, 
and  the  angle  C  M  E  is  her  parallax  at  the  Cape  of 
Good  Hope. 

The  sum  of  the  moon's  parallaxes  at  Greenwich  and 
at  the  Cape  of  Good  Hope  is  evidently  equal  to  the 
angle  G  M  C.  The  method  by  which  the  moon's  dis- 
tance is  actually  found  is  as  follows.  From  a  knowledge 
of  the  earth's  dimensions,  the  length  of  £  G  is  known 
with  considerable  accuracy.  And  though  the  plumb-line 


72  ASTRONOMY. 

at  G  is  not  directed  actually  to  the  earth's  centre,  E,  but 
in  a  slightly  different  direction,  H'  G  J?,  yet  from  know- 
ing the  form  of  the  earth,  we  can  calculate  accurately 
how  much  it  is  inclined  to  the  line  H  £,  which  is  di- 
rected to  the  earth's  centre.  Then  we  know  the  angle 
H'  G  Hy  and  we  have  observed  the  angle  H'  G  M  with 
the  mural  circle,  and  their  difference  is  the  angle  H  G  M, 
which  is  therefore  known.  The  difference  between  180° 
and  the  angle  H  G  M  gives  the  angle  E  G  M.  Then 
we  assume,  for  trial,  a  value  of  the  distance  E  M.  With 
the  length  E  M,  the  length  G  E,  and  the  angle  E  G  M, 
it  is  easy  to  compute  the  angle  G  M  E*  The  same 
process  is  used  to  calculate  the  angle  C  M  E.  We  then 
add  these  two  calculated  angles  together,  and  rind  whether 
their  sum  is  equal  to  the  angle  G  M  C,  which  we  have 
found  from  observation.  If  their  sum  is  not  equal  to 
this  angle  found  from  observation,  we  must  try  another 
assumption  for  the  length  of  E  M,  and  go  through  the 
calculation  again  ;  and  so  on  till  the  numbers  agree. 

We  supposed  at  first  that  the  observations  were  made 
at  the  same  instant  at  Greenwich  and  at  the  Cape  of 
Good  Hope.  This  is  not  strictly  correct;  but  the  dif- 
ference of  time  is  known,  and  the  moon's  motion  is  well 
enough  known  to  enable  us  to  compute  how  much  the 
angle  P'  C  M  changes  in  that  time ;  and  thus  we  know 
what  would  have  been  the  direction  of  the  line  C  M,  if 
the  observations  had  been  made  at  exactly  the  same  in- 
stant as  the  observation  at  G. 

When  now  we  wish  to  know  the  position  of  the  moon 
at  any  observation  as  seen  from  the  centre  of  the  earth, 
its  parallax  must  be  computed  and  applied.  By  correct- 
ing the  observed  place  of  the  moon  for  parallax,  it  has 
been  found  that  the  plane  of  the  moon's  orbit  passes 
through  the  centre  of  the  earth  in  the  same  way  as  the 

*  See  Appendix,  I.  6. 


ASTRONOMY.  73 

orbits  of  the  earth  and  of  the  other  planets  pass  through 
the  centre  of  the  sun. 

65.  Another  Method  of  finding  the  Difference  in  the  Di- 
rection of  the  two  Telescopes  pointed  at  the  Moon.  —  The 
method  given  above  for  ascertaining  the  difference  of  the 
direction  of  the  two  telescopes  when  turned  towards  the 
moon,  is  liable  to  only  one  error.  Since  the  inclination 
of  these  lines  is  determined  by  observations  made  with 
the  mural  circle,  it  is  necessary  that  every  observation 
should  be  corrected  for  refraction,  which,  as  we  have 
seen,  causes  objects  in  every  part  of  the  heavens  to  ap- 
pear higher  than  they  really  are.  Now  this  correction 
is  very  troublesome,  since  the  amount  of  refraction 
changes  with  the  altitude  of  the  object  and  with  the  dif- 
ferent conditions  of  the  atmosphere.  Prof.  Airy,  the  As- 
tronomer Royal  of  England,  says  that  refraction  is  the 
very  abomination  of  astronomers.  It  changes  with  the 
condition  of  the  atmosphere  in  so  irregular  a  manner 
that  every  correction  made  for  it  is  liable  to  a  slight 
error. 

There  is  another  way  of  ascertaining  the  difference  of 
direction  of  the  lines  G  M  and  C  M,  which  is  liable  to 
error  from  refraction  to  a  much  less  extent. 

We  have  already  seen  that,  if  the  telescopes  at  the 
two  observatories  are  pointed  to  the  same  fixed  star,  their 
direction  will  be  precisely  the  same.  If,  then,  a  fixed 
star,  S,  be  chosen,  which  is  quite  near  the  moon,  and 
which  comes  upon  the  meridian  at  nearly  the  same  time, 
and  the  telescope  of  the  mural  circle  at  each  station  be 
first  directed  to  this  star,  and  then  turned  to  the  moon, 
we  shall  get  the  inclination  of  each  of  the  directions 
G  M  and  C  M  to  the  direction  G  S.  The  difference  of 
their  inclinations  to  this  direction  will  evidently  be  their 
inclination  to  each  other.  Suppose,  for  instance,  that  at 
G  the  moon  is  seen  two  degrees  below  the  star,  and  at 
7 


74  ASTRONOMY. 

C  half  a  degree  below  it;  the  two  lines  G  M  and  C  J/ 
will  evidently  be  inclined  to  each  other  ij°.  As  the 
moon  and  star  must  be  observed  at-  very  nearly  the  same 
altitude,  and  under  almost  precisely  the  same  conditions 
of  the  atmosphere,  refraction  can  make  no  appreciable 
difference  in  their  angular  distance  from  each  other. 


SUMMARY. 

The  ancients  ascertained  the  distance  of  the  moon 
with  considerable  accuracy  by  the  observation  of  her 
eclipses.  (61.) 

The  distance  of  the  moon  is  now  found  by  means  of 
parallax.  (62.) 

Parallax  is  the  difference  of  direction  of  any  body  as 
seen  from  two  different  places. 

We  really  determine  the  distance  of  ordinary  bodies 
by  means  of  parallax. 

When  a  telescope  at  Greenwich  and  another  at  the 
Cape  of  Good  Hope  are  pointed  at  the  moon,  their  dif- 
ference of  direction  can  be  ascertained,  either  by  meas- 
uring the  polar  distance  of  the  moon  at  both  observa- 
tories (63),  or  by  measuring  at  both  observatories  the 
angular  distance  of  the  moon  from  a  fixed  star  near  her. 

(65.) 

The  parallax  of  the  moon  is  the  difference  of  her  direc- 
tion as  seen  from  the  centre  and  from  the  surface  of 
the  earth. 

When  the  difference  of  direction  of  two  telescopes 
which  have  been  pointed  at  the  moon  from  the  observa- 
tories at  Greenwich  and  the  Cape  of  Good  Hope  has 
been  ascertained,  the  parallax  of  the  moon  is  found  by 
the  method  of  trial  and  error.  (64.) 


ASTRONOMY.  75 


A  GENERAL  SURVEY  OF  THE  ORBITS  OF 
THE  PLANETS. 

66.  The  Inclination  of  the  Orbits  of  the  Planets  to  the  Plane 
of  the  Ecliptic.  —  We  have  now  learned  that  the  earth 
and  all  the  planets  revolve  about  the  sun  from  west  to 
east ;  that  each  describes  a  curve  called  an  ellipse,  one  of 
whose  foci  is  occupied  by  the  sun;  and  that  the  plane 
of  this  orbit  always  passes  through  the  centre  of  the 
sun.  Also  that  each  planet  moves  at  such  a  rate  in  dif- 
ferent parts  of  its  orbit  that  a  line  joining  the  planet 
with  the  sun  always  sweeps  over  equal  areas  in  equal 
times;  consequently  the  planets  all  move  faster  in  their 
orbits  at  perihelion  than  at  aphelion.  We  have  found, 
also,  that  the  different  planets  move  at  such  rates  that 
the  squares  of  their  periodic  times  bear  the  same  ratio  as 
the  cubes  of  their  mean  distances  from  the  sun.  We 
have  learned,  too,  that  these  ellipses  differ  in  form,  some 
being  .flatter  than  others ;  also  in  the  direction  of  their 
major  axes,  and  in  their  inclination  to  the  ecliptic. 

The  orbits  of  the  larger  planets  are,  however,  but 
slightly  inclined  to  the  ecliptic,  as  Figure  32  shows.  E 


represents  the  plane  of  the  ecliptic ;  yt  the  plane  of  Ju- 
piter's orbit ;  JVt  Neptune's;  V,  Venus's ;  My  Mercury's. 
P  is  the  plane  of  the  orbit  of  Pallas,  one  of  the  minor 
planets. 

67.  Nodes.  —  As  the  orbits  of  all  the  planets  are  some- 


76  ASTRONOMY. 

what  inclined  to  the  ecliptic,  they  must  all  intersect  it. 
The  points  at  which  they  intersect  the  ecliptic  are  called 
the  nodes  of  their  orbits. 

68.  Transits  of  Venus.  —  The  considerable  inclination 
of  the  orbit  of  Venus  to  the  ecliptic  explains  why  the 
transits  of  Venus  occur  so  seldom.  This  will  be  made 
clear  by  Figure  33.  S  represents  the  position  of  the  sun ; 

Fig.  33- 


V  V  V",  the  orbit  of  Venus ;  and  E  E'  E",  the  orbit 
of  the  earth,  that  is,  the  plane  of  the  ecliptic.  Now  it  is 
evident  from  inspection  of  the  figure  that  Venus  will  not 
be  seen  from  the  earth  to  cross  the  disc  of  the  sun,  unless 
the  earth  be  very  near  one  of  the  nodes  of  Venus's  orbit, 
as  at  E' ',  at  the  time  of  inferior  conjunction. 


HOW  TO   FIND   THE   DISTANCE   OF   THE 
FIXED    STARS. 

69.  We  have  already  seen  that  two  telescopes  so  far 
apart  as  those  at  the  observatories  at  Greenwich  and  at 
the  Cape  of  Good  Hope  do  not  sensibly  differ  in  direc- 
tion when  each  is  turned  to  the  same  fixed  star ;  so  that 
we  cannot  estimate  the  distance  of  the  stars  by  the  method 
employed  in  finding  the  distance  of  the  moon. 

It  will  be  remembered  that,  in  our  first  illustration  of 
parallax  (62),  we  were  enabled  to  estimate  the  distance 
of  the  candle,  either  by  turning  both  of  the  eyes  upon  it  at 
the  same  time  and  so  becoming  aware  of  their  difference 
of  direction,  or  by  using  only  one  eye  and  moving  the 
head,  and  so  becoming  aware  of  the  amount  by  which 


ASTRONOMY.  77 

the  eye  must  change  its  direction  for  a  given  movement 
of  the  head,  to  be  still  turned  toward  the  candle.  The 
first  method  of  estimating  the  distance  of  the  candle  was 
imitated  in  ascertaining  the  distance  of  the  moon.  Can 
we  ascertain  the  distance  of  the  fixed  stars  by  imitating 
the  second?  In  sweeping  round  the  sun  the  earth,  as 
we  have  seen,  describes  an  ellipse,  whose  mean  diameter 
is  some  190,000,000  of  miles.  Can  we,  by  using  the  tel- 
escope of  the  observatory  at  Greenwich  as  a  single  eye, 
estimate  the  distance  of  a  fixed  star  by  observing  how 
much  the  direction  of  the  telescope  must  be  changed  in 
order  always  to  point  to  that  star  when  on  the  meridian 
throughout  an  entire  revolution  of  the  earth  ?  Suppose 
that  the  north  polar  distance  of  a  fixed  star  be  measured 
by  means  of  the  mural  circle  at  Greenwich,  and  six  months 
from  this  time,  when  that  observatory  has  moved  away 
from  its  former  position  190,000,000  miles,  its  north  polar 
distance  be  measured  again.  If  the  polar  distances  of 
the  star  thus  measured  differ,  their  difference  must  be 
the  diiference  of  direction  of  the  telescope  at  the  two 
observations. 

70.  Does  the  Earth's  Axis  always  point  in  the  same  Di- 
rection?—  But  since  these  observations  are  made  at  long 
intervals,  it  becomes  necessary  to  know  whether  the  pole 
of  the  heavens  from  which  the  angular  distance  of  the 
star  is  measured  remains  unchanged  during  the  year.  It 
must  be  borne  in  mind  that  the  pole  of  the  heavens  is 
that  part  of  the  heavens  to  which  the  axis  of  the  earth 
points.  Now  we  must  ascertain  whether  the  axis  of  the 
earth  always  points  to  exactly  the  same  part  of  the  heav- 
ens, or  not ;  that  is,  whether  the  axis  of  the  earth  always 
points  in  exactly  the  same  direction.  That  the  axis  of 
the  earth  always  points  in  very  nearly  the  same  direction 
is  evident  from  the  fact  that  the  pole  of  the  heavens  does 
not  sensibly  change  its  position  from  year  to  year.  But 


78  ASTRONOMY. 

we  have  already  noticed  the  fact  (20)  that  the  points 
where  the  equator  cuts  the  ecliptic  are  slowly  shifting 
along  the  ecliptic  to  the  westward  at  the  rate  of  50"  an- 
nually. It  is  also  found  by  observation  that  the  incli- 
nation of  the  celestial  equator  to  the  ecliptic  does  not 
change.  Let  us  suppose  that  a  top,  with  its  upper  sur- 
face perfectly  flat,  be  spinning  upon  a  perfectly  level 
surface.  After  a  time,  the  end  of  the  handle  of  the  top 
will  be  seen  to  describe  a  small  circle,  and  the  upper 
surface  of  the  top  will  then  be  seen  to  be  inclined  at  a 
certain  angle  to  the  floor.  Suppose  now  that  the  top 
keep  on  spinning  for  a  time,  and  that  the  inclination  of 
the  upper  surface  of  the  top  to  the  floor  remain  the  same. 
Conceive  a  plane  parallel  with  the  floor  passing  through 
the  point  of  contact  of  the  handle  with  the  top.  This 
plane  may  represent  the  ecliptic ;  the  upper  surface  of 
the  top  may  represent  the  plane  of  the  earth's  equator ; 
and  the  points  where  the  circumference  of  the  upper  sur- 
face of  the  top  cuts  this  plane  may  be  considered  as 
the  equinoctial  points.  Now  as  the  top  goes  on  spin- 
ning, the  direction  of  its  inclination  to  the  floor  is  con- 
stantly shifting,  though  its  amount  remain  unchanged. 
It  is  evident,  then,  that  the  points  where  the  circumfer- 
ence of  this  surface  cuts  our  imaginary  ecliptic  are  con- 
tinually shifting,  and  that  they  will  pass  entirely  around 
while  the  end  of  the  top  handle  is  describing  a  circle. 
In  this  experiment  the  top  handle  represents  the  axis  of 
the  earth.  In  Figure  34  let  a  b  represent  the  ecliptic, 
and  efh  represent  the  position  of  the  equator  at  one 
time ;  then  g  k  I  must  represent  its  position  after  the 
equinoxes  have  shifted  from  h  to  /  and  from  e  to  g.  The 
shifting  of  the  equinoctial  points,  then,  seems  to  be  due 
to  a  shifting  of  the  direction  of  the  inclination  of  the 
earth's  equator  similar  to  that  of  the  upper  surface  of 
the  top  in  the  above  experiment.  If  this  is  really  so, 


ASTRONOMY. 


79 


the  end  of  the  axis  of  the  earth,   C  f,  ought  to  describe 
in  the  mean  time  an  arc,  Pf,  and  eventually  to  describe 


a  complete  circle  like  the  end  of  the  top  handle.  Now 
observation  reveals  the  fact  that  the  pole  of  the  heavens 
is  actually  describing  a  circle  in  the  heavens  whose  ra- 
dius is  an  arc  of  23^°,  and  that  it  is  describing  this  circle 
at  the  rate  of  50"  annually.  It  therefore  describes  a 
complete  circle  in  about  26,000  years.  The  earth,  then, 
as  it  spins  on  its  axis  in  its  journey  around  the  sun,  wab- 
bles like  a  spinning  top,  not  several  times  a  minute,  but 
once  in  26,000  years. 

Careful  observation  has  also  shown  that  the  earth's 
axis,  while  describing  this  circle  in  26,000  years,  has  a 
slight  tremulous  movement,  swinging  back  and  forth 
through  a  space  of  18"  in  nineteen  years.  The  effect 
of  both  these  movements  is  to  cause  the 
pole  of  the  heavens  to  describe  in  26,000 
years  such  a  curve  as  is  represented  in 
'Figure  35.  The  effect  of  the  first  move- 
ment of  the  axis  is  called  precession  ;  that 
of  the  second,  nutation. 

The  polar  distance  of  a  star  is  not  in 
any  case  changed  more  than  21"  by  pre- 


8o  ASTRONOMY. 

cession  and  nutation.  But  these  are  quantities  so  large 
that  we  must  be  perfectly  acquainted  with  their  laws  and 
magnitude  when  we  are  dealing  -  with  changes  in  the 
places  of  the  stars  not  exceeding  one  or  two  seconds. 

71.  The  Aberration  of  Light.  —  In  observing,  then,  the 
polar  distance  of  our  fixed  star  at  an  interval  of  six 
months,  we  must  allow  for  precession  and  nutation.  This 
can,  however,  be  done  with  the  greatest  accuracy.  Is 
there  anything  else  that  would  make  the  star  appear  in  a 
different  direction  at  the  end  of  the  six  months,  except 
the  change  of  position  of  the  observer?  On  a  rainy 
day,  when  the  drops  are  large  and  there  is  no  wind,  if 
one  goes  out  and  stands  still,  he  will  see  the  drops  of 
rain  falling  directly  downwards.  If  he  then  walks  for- 
ward, he  will  see  the  drops  fall  towards  him  ;  and  if  he 
walks  backward,  he  will  see  them  fall  away  from  him. 
Again,  in  Figure  36,  let  A  be  a  gun  of  a  battery,  from 
which  a  shot  is  fired  at  a  ship, 
D  E,  that  is  passing.  Let  A 
B  C  be  the  course  of  the  shot. 
The  shot  enters  the  ship's  side  at 
B,  and  passes  out  at  the  other 
side  at  C.  But  in  the  mean  time 
the  ship  has  moved  from  E  to  e, 
and  the  part  B  where  the  shot 
entered  has  been  carried  to  b. 
If  a  person  on  board  the  ship 
could  see  the  ball  as  it  crossed 

the  ship,  he  would  see  it  cross  in  the  diagonal  line  b  C. 
And  he  would  at  once  say  that  the  cannon  was  in  the 
direction  of  C  b.  If  the  ship  were  moving  in  the  oppo- 
site direction,  he  would  say  that  the  cannon  was  just  as 
far  the  other  side  of  its  true  position. 

Now  we  see  a  star  in  the  direction  in  which  the  light 
coming  from  the  star  appears  to  be  moving.     When  we 


e 


ASTRONOMY.  8 1 

examine  a  star  with  a  telescope  we  are  in  the  same  con- 
dition as  the  person  who  on  shipboard  saw  the  cannon 
ball  cross  the  ship.  The  telescope  is  carried  along  by 
the  earth  at  the  rate  of  eighteen  miles  a  second,  hence 
the  light  will  appear  to  pass  through  the  tube  in  a  slightly 
different  direction  from  that  in  which  it  is  really  moving ; 
just  as  the  cannon  ball  appears  to  pass  through  the  ship 
in  a  different  direction  from  that  in  which  it  is  really 
moving.  As  light  moves  with  enormous  velocity,  it  passes 
through  the  tube  so  quickly  that  it  is  apparently  changed 
from  its  true  direction  only  by  a  very  slight  angle,  but  it 
is  sufficient  to  displace  the  star.  This  apparent  change 
in  the  direction  of  light  caused  by  the  motion  of  the 
earth  is  called  aberration  of  light.  Now  as  it  is  at  once 
seen  that  the  earth  is  moving  in  opposite  directions  at 
the  beginning  and  the  end  of  six  months,  it  is  clear  that 
the  observations  must  be  corrected  for  aberration  as  well 
as  for  precession  and  nutation.  This  correction  can,  how- 
ever, be  made  with  great  accuracy,  since  we  can  compute 
the  exact  effect  of  this  disturbance.  There  however  re-- 
mains the  correction  for  refraction,  which  in  this  case  is 
more  troublesome  than  usual,  since  stars  which  are  on 
the  meridian  at  twelve  at  night  are,  six  months  from  that 
time,  on  the  meridian  during  the  day,  and  the  atmospheric 
conditions  which  affect  refraction  are  widely  different  by 
day  and  by  night. 

72.  By  this  method  the  inclination  of  the  directions 
of  a  telescope,  when  turned  to  a  bright  star  in  the  con- 
stellation of  the  Centaur  (Alpha  Centauri)  in  the  South- 
ern Hemisphere,  has  been  found  to  be  an  angle  of  about 
two  seconds  (Airy).  This  inclination  would  make  the 
distance  of  this  star  some  100,000  times  the  radius  of 
the  earth's  orbit,  which,  as  we  know,  is  about  95,000,000 
miles. 

An  angle  of  two  seconds  is  that  which  a  circle  of  T6<j  of 


8 1  ASTRONOMY. 

an  inch  in  diameter  would  subtend  at  the  distance  of  a 
mile.  Yet  this  is  the  greatest  parallax  that  any  star  is 
found  to  have,  when  seen  at  opposite  parts  of  the  earth's 
orbit.  The  parallax  of  Vega,  in  the  constellation  Lyra, 
is  not  more  than  J  of  a  second ;  and  there  are  compar- 
atively few  of  the  stars  whose  parallax  is  above  TV  of  a 
second.  But  considering  the  uncertainty  of  refraction, 
Airy,  the  Astronomer  Royal  of  England,  says  that  the 
determination  of  a  parallax  of  T20-  of  a  second  by  the 
above  method  is  more  than  he  can  undertake  to  answer 
for. 

73.  Another  Method  of  finding  the  Parallax  of  a  Fixed 
Star.  —  In  consequence  of  this  uncertainty  another  method 
has  been  devised,  admitting  of  far  greater  accuracy ; 
namely,  by  comparing  two  stars  whose  declinations  are 
very  nearly  the  same.  This  method  is  very  similar  to 
that  which  is  used  for  measuring  the  distance  of  the 
moon. 

Suppose  that  two  stars  have  very  nearly  the  same  dec- 
lination, and  that  from  observation  by  the  first  method 
we  have  reason  to  suppose  that  one  of  the  stars  is  at 
such  an  enormous  distance  that  it  will  have  no  sensible 
parallax,  while  from  the  same  observation  we  have  reason 
to  believe  that  the  other  is  very  much  nearer.  If  now 
we  measure  the  angular  distance  between  the  two  stars 
at  opposite  points  of  the  earth's  orbit,  the  difference  of 
these  angular  measurements  will  be  the  parallax  of  the 
nearer  of  the  two  stars. 

By  this  method,  since  we  compare  stars  which  are 
seen  very  nearly  in  the  same  direction,  we  get  rid  of  the 
uncertainty  of  refraction,  and  also  of  precession,  nuta- 
tion, and  aberration ;  because  these  produce  the  same 
effect  on  both  stars.  This  is  the  method  which  the  cel- 
ebrated Bessel,  of  Konigsberg,  used  for  determining 
the  distance  of  the  small  star  known  as  61  Cygni.  He 


^ASTRONOMY.  83 

thus  found  the  parallax  of  this  star  as  seen  from  opposite 
parts  of  the  earth's  orbit  to  be  T%-  of  a  second ;  and  this 
corresponds  to  a  distance  of  660,000  times  the  radius  of 
the  earth's  orbit,  or  63,000,000,000,000  miles.  "  Enor- 
mous as  this  distance  is,"  says  Airy,  "I  state  it  as  my 
deliberate  opinion,  founded  upon  a  careful  examination 
of  the  whole  process  of  observation  and  calculation,  that 
it  is  ascertained  with  what  may  be  called  in  such  a  prob-  ' 
lem  considerable  accuracy."  The  distance  of  those  stars 
whose  parallax  is  estimated  at  TV  of  a  second  is  about 
2,000,000  times  the  distance  of  the  earth  from  the  sun. 

74.  The  Immensity   of  these  Distances.  —  We   have   no 
appreciation   of  distances  so  vast.     The   moon  has  been 
found  to  be  distant  from  the  earth  about  240,000  miles. 
If  a  locomotive  were  travelling  at  the  rate  of  1000  miles 
a  day  it  would  take  it  eight  months  to  reach  the  moon ; 
travelling  at  the   same   rate   it  would  reach   the  sun   in 
260  years,  and  the  star  61   Cygni  in   171,600,000  years, 
a  period  of  which  we  can  form  no  conception  whatever. 

Light,  it  will  be  remembered,  travels  at  the  rate  of 
about  *i 90,000  miles  a  second.  It  would  accordingly 
take  light  about  yj  years  to  reach  us  from  61  Cygni.  If 
this  star  were  suddenly  annihilated,  it  would  be  over 
seven  years  before  we  should  become  aware  of  it.  Yet 
this  is  one  of  the  nearer  fixed  stars.  It  has  been  esti- 
mated from  tolerably  accurate  measurements  that  it 
would  take  light  fourteen  years  to  reach  Us  from  Sirius, 
twenty  years  from  Vega,  and  twenty-five  years  from  Arc- 
turus ;  and  Sir  John  Herschel  has  estimated  that  light 
requires  at  least  2000  years  to  reach  us  from  the  smaller 
stars  with  which  the  Milky  Way  is  crowded. 

75.  Nebula.  —  Nor  is  this  all.     Near  the  belt  of  An- 
dromeda there  may  be  seen  with  the  naked  eye  a  faint 
glimmer  of  light  oh  a  very  clear  night.     Figure  37  shows 
this  object  as  it  appeared  in   Sir  John  Herschel's   tele- 


scope,  and  Figure  38  as  it  appears  in  the  powerful  re- 
fractor of  the  Observatory  at  Cambridge,  Mass.  Such 
an  object  is  called  a  nebula.  Nebulae  are  really  very  nu- 

Fig.  38- 


ASTRONOMY. 


merous,  though  very  few  of  them  are  bright  enough  to 
be  seen  with  the  unaided  eye. 


In  Figure  39   is  represented  the  celebrated   nebula  in 
the   constellation    of  Vulpecula,    as   it    appeared   to   Sir 


John  Herschel.     Figure  40  shows  the  same  nebula  as  it 
appears  in  the  great  reflecting  telescope  of  Lord  Rosse. 
8 


86 


ASTRONOMY. 

ITig.  41. 


Figure  41  represents  the  Crab  nebula  in  Taurus,  as  de- 
lineated by  Lord  Rosse ;  and  Figure  42,  the  great  nebula 
of  Orion,  as  figured  by  Professor  G.  P.  Bond  of  the  Cam- 
bridge Observatory.  Another  celebrated  nebula,  known 
as  the  Ring  nebula  in  Cygnus,  is  shown  in  Figure  43. 

About  five  thousand  nebulae  have  been  observed.  It  is 
seen  from  the  above  figures  that  they  differ  greatly  in  form. 
It  will  be  noticed  in  the  case  of  the  Dumb-bell  nebula 
(Figure  39),  and  also  in  the  Crab  nebula,  that  these  neb- 
ulae often  have  the  appearance  of  clusters  of  minute  stars 
when  viewed  with  very  powerful  telescopes.  This  has  led 
astronomers  generally  to  believe  that  many  of  the  neb- 
ulae are  vast  systems  of  stars  like  our  own,  seen  at  im- 
mense distances.  Figure  44  is  a  representation  of  what 
Sir  John  Herschel  conceived  would  be  the  appearance 


ASTRONOMY. 

Fi- 


Fig.  43- 


cf  our  system  of  stars  including  the  Milky  Way,  when 
seen  at  the  distance  of  one  of  the  nebulae.  According  to 
this  theory,  our  system  of  stars,  which  is  to  us  so  great 
that  we  can  have  no  appreciation  of  its  vast  dimensions, 
is  really  but  one  of  countless  systems  which  are  scattered 
throughout  space  at  such  distances,  that,  when  viewed 
from  one  another  with  the  most 
powerful  telescopes,  they  appear 
as  small  faintly  luminous  spots. 
We  now  begin  to  see  that  the 
supposition  which  we  made  a 
long  time  ago  (Part  First,  Sec- 
tion 4)  of  beings  small  enough 
to  dwell  on  a  molecule  of  a 
stone  as  we  dwell  upon  the 
earth,  is  after  all  not  so  very 


unreasonable.  For  as  we  gain  some  faint  conception  of 
the  dimensions  of  the  universe  as  a  whole,  we  feel  that  we 
are  such  minute  beings,  dwelling,  not  upon  a  molecule, 
but  upon  one  of  the  smallest  atoms  of  which  a  single  mole- 
cule of  the  universe  is  made  up.  But  the  greatest  wonder 
of  all  is  that  we,  after  measuring  but  a  small  fraction  of  the 
distance  around  our  atom,  and  making  a  few  simple  obser- 
vations of  the  position  of  the  heavenly  bodies,  can  then, 
by  simple  geometric  and  trigonometric  computation,  meas- 
ure the  dimensions  of  the  universe. 

76.  The  Nebulce  are  not  all  Systems  of  Stars.  —  It  is  not 
at  all  clear  as  yet  that  the  nebulae  are  all  systems  of  stars. 
While  it  seems  quite  certain  that  some  of  them  are  such 
systems  at  immense  distances,  there  are  strong  reasons 
for  believing  that  others  are  but  thin  clouds  of  luminous 
gases  which  may  be  much  nearer  the  earth  than  the 
nearest  fixed  star. 


SUMMARY. 

A  telescope  at  the  Cape  of  Good  Hope,  when  pointed 
at  a  fixed  star,  does  not  cliifer  appreciably  in  direction 
from  a  telescope  at  Greenwich  pointed  at  the  same  star. 


ASTRONOMY.  89 

If  a  telescope  is  turned  to  the  same  fixed  star  at  op- 
posite points  of  the  earth's  orbit,  the  difference  of  its 
direction,  if  appreciable,  can  be  found  by  measuring  the 
star's  polar  distance.  (69.) 

The  earth's  axis  has  a  slight  wabbling  motion,  which 
causes  the  celestial  pole  to  describe  a  circle  with  a  ra- 
dius of  23!°  in  about  26,000  years. 

This  movement  of  the  pole  is  called  precession. 

In  addition  to  its  regular  wabble,  the  earth's  axis  has 
a  tremulous  motion.  The  effect  of  this  motion  is  called 
nutation. 

In  an  exact  measurement  of  the  polar  distances  of  a 
star,  a  correction  must  be  made  for  the  effect  of  preces- 
sion and  nutation.  (70.) 

Aberration  of  light  is  the  apparent  change  in  the  di- 
rection of  light  caused  by  the  motion  of  the  earth  in  its 
orbit.  The  observation  of  a  star's  polar  distance  must 
also  be  corrected  for  aberration.  (71.) 

The  parallax  of  a  fixed  star  may  often  be  best  deter- 
mined by  measuring,  at  opposite  points  of  the  earth's 
orbit,  its  angular  distance  from  another  star  near  it.  (73.) 

It  takes  light  about  seven  years  to  come  to  us  from  the 
nearest  fixed  stars  of  our  system,  and  probably  several 
thousand  to  come  from  the  most  remote.  (74.) 

Many  of  the  nebulcz  are  supposed  to  be  outlying  sys- 
tems of  stars,  so  distant  that  they  appear  no  larger  than 
a  man's  fist,  yet  so  large  that  it  takes  light  several  thou- 
sand years  to  cross  them.  (75.) 

SYSTEMS   OF    SATELLITES   AND    SUNS. 

77.  Satellites. — We  have  already  seen  that  the  earth 
in  its  revolution  about  the  sun  is  attended  by  a  moon, 
which  revolves  about  it  as  a  centre.  Such  an  attendant 

is  called  a  satellite. 

8* 


90  ASTRONOMY. 

The  telescope  shows  that  Jupiter  is  accompanied  by  a 
system  of  four  satellites  revolving  about  him  as  a  centre, 
and  that  Saturn  is  accompanied  by  a  system  of  eight  sat- 
ellites, Uranus  by  a  system  of  four  (perhaps  six),  and 
Neptune  by  one  satellite. 

In  our  solar  system,  then,  we  have  satellites  revolving 
about  planets,  and  these  planets  with  their  systems  of 
satellites  revolving  about  the  sun.  Is  there  now  any 
evidence  that  the  sun,  with  this  complex  system  of  plan- 
ets and  satellites,  revolves  about  some  other  sun? 

78.  The  Motio?i  of  our  Solar  System  through  Space.  — 
We  have  heretofore  spoken  of  the  stars  as  fixed.  But 
upon  comparing  the  places  of  stars  as  we  observe  them 
in  different  years,  and  applying  the  corrections  for  pre- 
cession, nutation,  and  aberration,  so  as  to  reduce  every 
observation  of  every  star  to  what  it  ought  to  exhibit  on 
the  first  day  in  the  year,  agreeably  to  the  common  prac- 
tice of  astronomers,  we  find  that  the  vast  majority  of  the 
stars  which  have  been  well  observed  seem  to  have  a  mo- 
tion of  their  own.  This  motion  is  known  as  the  proper 
motion  of  the  stars.  In  all  good  catalogues  of  stars,  the 
direction  in  which  the  stars  appear  to  be  moving,  and 
the  amount  of  their  motion  in  a  year,  are  given.  This 
proper  motion  has  been  discovered  only  after  many  years' 
observations ;  it  is  in  every  case  a  small  quantity ;  yet 
in  most  instances  this  quantity  has  been  correctly  as- 
certained. The  proper  motions  of  Sirius  and  Arcturus 
are  pretty  large ;  but  the  largest  observed  are  those  of 
two  small  stars  known  to  astronomers  as  61  Cygtii  and 
Groombridge  1830.  The  motion  of  the  former  is  about 
five  seconds  a  year,  and  of  the  latter  nearly  seven  seconds. 
The  proper  motions  of  many  of  the  stars  are  very  irregular 
in  direction  and  magnitude,  but  with  regard  to  others  there 
is  a  certain  approach  to  regularity. 

If  you  are  walking  through  a  forest,  and  keep  your  at- 


ASTRONOMY.  91 

tention  on  the  objects  directly  in  front  of  you,  they  do  not 
appear  to  change  their  place ;  but  i-f  you  look  at  the  ob- 
jects to  the  right  or  to  the  left,  they  appear  to  be  spreading 
away  to  the  right  or  to  the  left.  Even  if  you  did  not  know 
that  you  were  moving  yourself,  yet  by  seeing  these  ob- 
jects spreading  away  you  could  infer  with  tolerable  cer- 
tainty that  you  were  moving  in  a  certain  direction.  Now 
if  it  should  appear  that,  taking  the  stars  generally,  we  can 
fix  on  any  direction  and  see  that  the  stars  in  that  direc- 
tion do  not  appear  to  be  moving,  but  that  the  stars  right 
and  left  appear  to  be  moving  away  from  that  point,  then 
there  is  good  reason  to  infer  that  we  are  travelling  toward 
that  point.  This  speculation  was  first  started  by  Sir 
William  Herschel.  He  found  a  point  in  the  heavens, 
in  the  constellation  Hercules,  such  that  the  great  ma- 
jority of  the  stars  about  the  point  have  no  sensible 
proper  motion,  while  the  stars  to  the  right  and  left  of  it 
have  apparently  a  motion  to  the  right  and  left  respec- 
tively. He  inferred  from  this  that  the  solar  system  is 
travelling  in  a  body  towards  this  point.  Every  astrono- 
mer who  has  examined  this  subject  carefully  has  come  to 
a  conclusion  very  nearly  the  same  as  that  reached  by  Sir 
William  Herschel ;  namely,  that  the  whole  solar  system 
is  moving  toward  that  point  in  the  constellation  Her- 
cules. 

It  is  probable,  then,  that  our  sun,  with  his  complex 
system  of  planets  and  satellites,  is  really  revolving  about 
some  other  sun,  whose  position  is  not  yet  ascertained. 

79.  Double  Stars.  —  There  is  in  the  vicinity  of  Vega, 
the  brightest  star  of  the  constellation  Lyra,  a  small  star 
called  Epsilon  Lyra,  which  appears  elongated  to  some 
persons  of  very  keen  eyesight,  and  this  appearance  sug- 
gests that  it  may  really  be  composed  of  two  luminous 
points.  It  is  only  necessary  to  examine  it  with  an  opera- 
glass  to  see  that  it  really  consists  of  two  stars,  separated 


9^  ASTRONOMY. 

by  an  interval  equal  to  about  a  ninth  part  of  the  appar- 
ent diameter  of  the  moon. 

Here,  then,  we  have  an  example  of  an  easily  divided 
double  star,  which  a  keen  eye  or  an  opera-glass  of  small 
magnifying  power  is  sufficient  to  separate  into  its  com- 
ponents. If  now  we  examine  each  of  these  components 
with  an  instrument  of  considerable  optical  power,  we  find 
that  each  consists  of  two  stars  so  near  together  that  the 
intervals  separating  them  are  not  more  than  the  seventieth 
part  of  the  total  distance  of  the  couples  themselves  :  so 
that  we  have  here  a  double-double  star,  or  a  quadruple  star. 
A  star  which  appears  single  to  the  naked  eye  becomes 
quadruple  when  examined  with  a  powerful  telescope. 

A  century  ago  only  about  twenty  double  stars  were 
known ;  now,  however,  we  have  catalogues  of  more  than 
six  thousand. 

80.  This  Union  of  two  Stars  is  not  in  all  cases  Accidental. 
—  The  first  impression  is  that  this  proximity  of  two  or 
more  stars  is  purely  accidental,  being  due  to  an  effect 
of  perspective ;  the  stars  themselves,  though  differing 
widely  in  their  distance  from  us,  lying  in  the  same  line 
of  sight. 

When,  however,  these  double  stars  are  carefully  scru- 
tinized, it  is  found  that  in  some  cases  their  components 
have  the  same  proper  motion,  while  in  other  cases  they 
do  not.  Again,  those  whose  components  have  the  same 
proper  motion  are  often  found  to  revolve  about  each 
other  in  periods  of  greater  or  less  length,  while  nothing 
of  the  kind  is  observed  in  the  other  class.  Hence 
double  stars  have  come  to  be  classified  as  optical  and 
physical  pairs.  Those  whose  components  do  not  have 
the  same  proper  motion,  and  do  not  revolve  about  one 
another,  are  regarded  as  optical  pairs,  or  optically  double 
stars.  Their  apparent  proximity  is  regarded  as  purely 
accidental,  owing  to  the  fact  that,  though  they  are  at 


ASTRONOMY.  93 

very   different  distances  from  us,   they  happen   to  be  in 
very  nearly  the  same  direction. 

Those  whose  components  have  the  same  proper  mo- 
tion, or  have  been  observed  to  revolve  about  one  another, 
are  supposed  to  be  about  the  same  distance  from  the 
earth  and  to  be  physically  connected,  so  as  to  form  sys- 
tems like  that  of  the  sun  and  the  planets.  These  are 
called  physical  pairs,  or  physically  double  stars. 

8 1.  Theta  Orionis.  —  There  is  a  remarkable  system  of 
stars  in  the  constellation  of  Orion,  near  the  centre  of  the 
great  nebula  already  mentioned.     The  unaided  sight  dis- 
tinguishes this   system  only   as  a  luminous  point.     With 
the  help  of  a  good  telescope,  however,  this  point  is  di- 
vided into  four  stars,  which  are  seen  in  the  form  of  a  tra- 
pezium.    When  viewed  with  a  telescope  of  five  or  six  inch 
aperture,  two  of  the  stars  of  the  trapezium  are  seen  to 
be  accompanied  by  two  other  very  small  stars,  forming 
altogether  a  group  of  six  stars,  as  shown  in  Figure  45. 

This  sextuple  star,  known 
as  Theta  Orionis,  or  more  _____ 
commonly  as  the  trape- 
zium of  Orion,  probably 
constitutes  a  real  system, 
since  the  five  smaller  stars 
have  the  same  proper  mo- 
tion as  the  principal  one. 
Mr.  Lassell  has  discovered 
a  seventh  star  in  this  re- 
markable system,  so  that  Theta  Orionis  is  a  septuple  star. 

82.  Xi    Ursa   Majoris. —  In    the   constellation    of  the 
Great  Bear,  or  Ursa  Major,  there  is  a  star,  designated  in 
the  catalogues  by  the  Greek  letter  £,   or  Xi,  which  has 
been  known   as  a  double  star  since    1782.     One  of  the 
components  of  this  system  is  of  the  fourth,  the  other  of 
the  fifth,  magnitude.     The  movement  of  revolution  of  the 


94  ASTRONOMY. 

second  around  the  first  having  been  detected,  a  French 
astronomer,  Savary,  determined  by  .calculation  the  ele- 
ments of  the  orbit.  The  period  of  revolution  is  sixty-one 
years.  Since  the  discovery  of  the  system,  then,  one  rev- 
olution has  been  completed,  and  more  than  a  third  of 
another. 

The  elliptical  or  oval  form  of  the  orbit  of  this  binary 
system  is  very  decided.  It  is  much  more  elongated  than 
that  of  any  of  the  planets  of  the  solar  system.  But 
among  the  double  stars  there  are  some  whose  orbits  are 
even  more  elongated.  Such  is  that  of  Alpha  Centauri, 
whose  period  of  revolution  exceeds  seventy-eight  years. 
The  orbits  of  all  the  binary  stars,  so  far  as  known,  are 
ellipses,  like  those  of  the  planets. 

83.  Other  Binary  Stars  and  their  Periods.  —  The  fol- 
lowing are  a  few  of  the  double  stars  whose  periods  have 
been  determined :  — 

Zeta  Herculis  36  years 

Zeta  Cancri  59     " 

Mu  Coronae  Borealis  66     " 

70  Ophiuchi  93     " 

Gamma  Virginis  150     " 

6 1  Cygni  450     " 

There  is,  as  seen  by  this  table,  great  variety  in  the  pe- 
riods of  double  stars.  But  there  are  others  whose  periods 
probably  differ  even  more  widely.  In  Berenice's  Hair, 
and  in  the  Lion,  there  are  two  pairs,  the  first  of  which 
seems  to  have  a  period  of  twelve  years,  while  the  second 
seems  to  have  a  period  of  twelve  centuries. 

84.  The  Dimensions  of  the  Orbits  of  Binary  Stars.  — 
When  we  know  the  distance  of  the  binary  stars,  we  can 
calculate,  not  only  the  form  of  their  orbits  and  their  pe- 
riods of  revolution,  but  also  the  dimensions  of  their  orbits. 
It  has  been  calculated  that  the  mean  distance  between 


ASTRONOMY.  95 

• 

the  components  of  Alpha  Centauri  is  not  less  than 
i  319,000,000  miles.  The  mean  distance  of  the  compan- 
ion of  6 1  Cygni  is  about  forty-five  times  the  length  of 
the  radius  of  the  earth's  orbit. 

Of  the  six  thousand  double  stars  six  hundred  and  fifty 
have  been  demonstrated  to  be  physically  connected  systems. 

85.  The  Sun  as  a  Fixed  Star.  —  If  now  we  imagine 
the  sun  to  be  plunged  into  space  to  the  distance  of  the 
nearest  fixed   star,   and  calculate,   according  to   the   laws 
of  optics,  what  will  be  the  diminution  of  its  light,  we  find 
that  it  would  become  of  the  brightness  of  a  star  of  the 
second  magnitude,  that  is,  it  would  shine  with  the  bril- 
liancy of  the  Pole  Star,  or  of  the  principal  stars  in  the 
constellation  of  the  Great  Bear. 

86.  The  Heavenly    Bodies    are    all    in    Motion.  —  The 
stars,   then,   are  manifestly   suns,   and  the   double,   triple, 
sextuple,  and  other  multiple  stars  are  systems   of  revolv- 
ing suns.      Each  of  these  suns  is  probably  attended  by 
systems  of  planets  like  our  own,  which  of  course  could 
not  be   seen    at   their   immense    distance   with   the   most 
powerful  telescope.     It  would  seem  that  all  the  heavenly 
bodies    are    in    motion,    satellites    about    planets,    planets 
about   swns,   and  suns  about  suns,  and  systems  of  suns 
about  systems  of  suns ;  and  that  the  reason  why  we  do 
not  detect  this  motion  in  all  cases  is  that  the  stars  are 
situated   at   such   enormous    distances   that   their  motion 
cannot   be   detected  in  the  brief  space  of  two  or  three 
thousand  years  which  has  elapsed  since  recorded  obser- 
vations first  began. 

We  have  already  seen  that  the  proper  motion  of  the 
stars  amounts  at  most  to  about  seven  seconds  a  year, 
and  these  are  probably  the  very  nearest  fixed  stars.  Yet 
from  their  known  distance  and  proper  motion  it  has  been 
computed  that  the  following  stars  must  move  at  the 
rates  given  below  :  — 


96  ASTRONOMY. 

Arcturus  54  miles  a  second. 

6 1  Cygni  40       " 

Capella  30      '« 

Sinus.  14       "  " 

Alpha  Centauri  13       "  " 

Vega  13       "  " 

It  will  be  remembered  that  the  earth's  velocity  in  its 
orbit  is  eighteen  miles  a  second.  Notwithstanding  this 
enormous  velocity,  it  has  required  years  of  patient  ob- 
servation to  establish  the  fact  of  the  proper  motion  of 
the  stars.  We  need  not  be  surprised,  then,  that  the 
more  remote  stars  appear  fixed,  though  they  may  be 
moving  at  the  enormous  rate  of  fifty  miles  a  second. 


SUMMARY. 

Many  of  the  planets  are  accompanied  by  systems  of 
satellites. 

Our  solar  system  is  a  complex  system  of  planets  and 
satellites.  (77.) 

Our  sun  is  travelling  through  space. 

Many  of  the  so-called  fixed  stars  have  proper  motions. 

(78.) 

Stars  which  appear  close  together  and  have  the  same 
proper  motion  constitute  a  physical  system.  (80.) 

Theta  Orients  is  a  remarkable  system  of  this  kind.    (81.) 
The  components  of  these  systems  are  in  many  cases 
known   to   revolve   about   a   common   centre   in  elliptical 
orbits.     (82-84.) 


II. 


PHYSICAL  FEATURES  OF  THE 
HEAVENLY  BODIES. 


PHYSICAL   FEATURES   OF  THE 
HEAVENLY    BODIES. 


THE    SUN. 

WE  have  seen  that  the  universe  is  made  up  mainly  of 
satellites,  planets,  and  suns,  and  we  have  learned  some- 
thing of  the  motions  and  distances  of  these,  and  have 
thus  got  a  general  notion  of  the  structure  of  the  universe 
as  a  whole.  We  now  turn  our  attention  to  these  bodies 
to  inquire  what  is  known  of  each  individually.  We  nat- 
urally begin  at  the  centre  of  the  solar  system. 

87.  The  Size  of  the  Sun. — We  have  already  learned 
that  the  sun  is  distant  from  the  earth  about  95,000,000 
miles.  Its  disc  is  well  known  to  be  circular,  and  careful 
measurement  shows  that  it  is  an  exact  circle. 

Knowing  the  distance  of  the  sun,  it  is  an  easy  problem 
to  find  its  size.  Suppose  a  pasteboard  disc,  say  about 
four  inches  in  diameter,  be  held  before  the  sun,  it  will  be 
found  that  it  must  be  held  about  twelve  yards  from  the 
eye  in  order  exactly  to  cover  the  sun's  disc.  Now  since 
the  distance  between  the  lines  in  Figure  46.  et  any  two 

Fig.  46- 


points   is   evidently  proportioned  to   their  distance    from 
the  vertex  of  the  angle  which  the  lines  make,  it  follows 


IOO 


ASTRONOMY. 


that  twelve  yards  is  to  95,000,000  miles  as  four  inches  is 
to  the  diameter  of  the  sun. 

We  thus  learn  that  the  diameter  of  the  sun  is  about  112 
times  the  diameter  of  the  earth,  or  887,076  miles.  The  cir- 
cumference of  the  sun,  therefore,  exceeds  2,785,400  miles. 

We  have  already  seen  that  the  moon's  mean  distance 
from  the  earth  is  about  thirty  times  the  earth's  diameter. 
If,  then,  we  imagine  the  centre  of  the  sun  to  be  at  the 
centre  of  the  earth,  his  circumference  would  extend  be- 
yond the  orbit  of  the  moon  by  a  distance  equal  to  twenty- 
six  diameters  of  the  earth. 

In  Figure  47,  the  inner  circle  represents  the  size  of  the 
earth,  the  middle  one  the  moon's  orbit,  and  the  outer  one 
the  size  of  the  sun,  all  drawn  to  the  same  scale.  The 


Fig.  47- 


ASTRONOMY. 

volume  of  the  sun  is  about  a  million  and  a  half  times  that 
Df  the  earth. 

88.  The  Sun-Spots.  —  When  the  sun  is  examined  with 
\  telescope  of  moderate  magnifying  power,  the  eye  being 
properly  protected,  his  disc  usually  appears  sprinkled  with 
irregularly  grouped  dark  points.  These  dark  spots  are 
the  sun-spots. 

Figure  48  gives  an  idea  of  the  manner  in  which  the 
spots  are  distributed,  and  their  grouping  at  any  one 
time. 

Fig.  48- 


The  number  of  the  spots,  their  relative  positions,  and 
their  forms  are  found  to  vary  continually.  Sometimes, 
though  rarely,  the  solar  disc  is  free  from  them  j  and  some- 
times as 'many  as  eighty  spots  have  been  visible  at  once. 
From  a  series  of  observations  continuing  through  a  pe- 
riod of  some  forty  years,  it  appears  that  the  spots  occur 
with  greater  frequency  at  regular  intervals.  They  dimin- 
ish in  number  during  five  or  six  years,  and  then  increase 
again  through  about  the  same  length  of  time.  Their 
greatest  number  thus  occurs  at  intervals  of  ten  or  twelve 
years.  The  last  maximum  was  in  1860. 


ASTRONOMY. 


89.  The  Motion  of  the  Spots.  —  When  observed  with  care 
during  several  consecutive  days,  the  spots  are  seen  to 
vary  in  fjoth  form  and  position.'  But  amidst  all  their 
variations,  a  common  movement  of  the  whole  in  the 
same  direction  can  be  distinguished. 

Let  us  suppose  a  spot  to  appear  on  the  eastern  edge 
or  limb  of  the  sun.  From  day  to  day  it  will  be  seen  to 
progress  with  increasing  rapidity  until  it  occupies  a  cen- 
tral position  on  the  disc.  It  still  continues  to  advance, 
but  now  with  decreasing  rapidity,  until  it  finally  disap- 
pears on  the  western  border.  The  same  is  true  of  all 
the  spots,  which  at  first  appear  scattered  over  the  sun's 
disc.  They  all  describe,  in  the  same  direction,  with  nearly 
equal  velocities,  either  straight  lines,  or  curved  ones  whose 
convexity  always  lies  in  the  same  direction  for  all  the 
spots  observed  at  the  same  time. 

Let  us  suppose  that  the  particular  spot  that  we  have 
observed  is  of  an  oval  form,  its  greatest  length  being  at 
right  angles  to  the  direction  of  its  motion  across  the 
sun's  disc  at  the  moment  when  it  appeared  on  the  east- 
ern limb.  As  it  approaches  the  centre  the  spot  widens, 
until  at  the  centre  it  becomes  nearly  circular  ;  then,  hav- 
ing passed  the  centre,  its  form  becomes  more  and  more 
oval  again  until  its  disappearance,  its  apparent  size  in  one 
direction  meanwhile  not  having  sensibly  changed.  Fig- 
ure 49  shows  these  changes  of  form  during  the  first  and 
last  half  of  the  period  of  the  visibility  of  the  spot. 

Fig.  49. 


About  fourteen  days  is  the  time  during  which  the  spots 


ASTRONOMY. 


remain  visible,  and  this  time  is  nearly  the  same  for  all, 
though  they  do  not  all  traverse  arcs  of  the  same  length 
on  the  sun's  surface. 

It  is  also  fourteen  days  after  the  disappearance  of  a 
spot  on  the  western  border  before  it  appears  again  on  the 
eastern,  often  changed  in  form,  yet  generally  recognizable. 

Precise  measurements  have  proved  both  the  general 
uniformity  and  the  parallelism  of  these  movements. 

90.  The  Spots  are  not  Planets.  —  It  was  at  first  thought 
that  these  spots  might  be  caused  by  small  planets  revolv- 
ing about  the  sun  and  presenting  to  us  their  unillumined 
faces.     But  since  the  time  of  their  disappearance  is  equal 
to   that   of  their  visibility,   they  cannot  be  such  planets. 
For  it  is  evident  from  Figure  50   that,   were  they  such 
planets,    they    would    remain    invisible 

longer  than  they  are  visible.  For  such 
a  planet  would  be  visible  only  while  de- 
scribing the  arc  A  B  across  the  sun's 
disc,  while  it  would  be  invisible  while 
describing  the  much  longer  arc  A  C  B. 
It  was  also  thought  possible  to  explain 
the  movements  of  the  spots  from  the  t 
eastern  to  the  western  border,  by  an  act- 
ual translation  of  them  across  the  sur- 
face of  the  sun,  the  surface  itself  being 
immovable.  This  supposition  is,  how- 
ever, inconsistent  with  their  uniformity 
of  movement. 

91.  The  Sun's  Rotation  on  his  Axis. — 
The  movements  of  the  spots,  then,  show 

beyond  a  doubt  that  the  sun  is  rotating  on  an  axis  from 
west  to  east.  The  change  of  form  of  the  spots  illus- 
trated in  Figure  49,  and  their  unequal  rate  of  motion 
on  different  parts  of  the  sun's  disc,  also  prove  beyond 
a  doubt  that  the  sun's  surface  is  spherical.  These 


ASTRONOMY. 


Fig.  Si- 


changes  of  form  and  of  speed  are  the  effect  of  perspec- 
tive. The  sun,  then,  like  the  earth,  is  not  only  moving 
through  space,  but  whirls  on  its  axis  as  it  moves. 

We  have  already  stated  that  the  interval  between  two 
successive  appearances  of  the  same  spot  on  the  same 
edge  of  the  sun  is  tvyenty-eight  days.  The  period  of  ro- 
tation of  the  sun  is  less  than  this.  This  will  be  evident 
by  a  reference  to  Figure  51. 

Let  S  be  the  centre  of  the 
sun ;  a  the  position  of  a  spot ; 
and  E  the  position  of  the 
earth.  The  spot  will  then 
appear  on  the  centre  of  the 
sun.  The  sun  will  evidently 
have  made  a  complete  rota- 
tion when  the  spot  comes 
upon  the  line  S  E  again,  but 
it  will  not  appear  in  the 
centre  of  the  sun  till  it  comes 
on  the  line  S  F,  since  the 
earth  has  in  the  mean  time 
passed  from  E  to  F. 

Between  the  two  successive 
appearances  of  the  same  spot 
upon  the  centre  of  the  sun, 
the  sun  will  have  more  than 

completed  a  rotation.  Since  we  know  the  angular  veloci- 
ty of  the  earth  in  its  orbit,  we  can  find  how  much  more 
than  a  rotation  the  sun  has  completed.  For  he  will  evi- 
dently have  completed  a  rotation  plus  the  angular  space 
that  the  earth  has  passed  over  in  twenty-eight  days.  It 
is  thus  found  that  the  sun  rotates  on  its  axis  once  in 
about  twenty-five  days. 

92.  The  Axis  of  the  Sun  is  not  perpendicular  to  the  Plane 
of  the  Ecliptic.  —  If  the  axis  of  the  sun  were  perpendicular 


ASTRONOMY. 


105 


to  the  plane  of  the  ecliptic,  the  spots  would  evidently  ap- 
pear always  to  describe  straight  lines  across  the  sun's  disc. 
Observation  shows  that  twice  in  the  year  they  describe 
straight  lines  across  the  sun,  and  that  for  half  of  the  re- 
maining time  they  describe  curves  which  are  convex  to- 
wards the  upper  limb  of  the  sun,  and  the  other  half  curves 
which  are  convex  towards  the  lower  limb  of  the  sun,  as 
shown  in  Figure  52.  It  has  thus  been  found  that  the 
sun's  axis  is  inclined  82°  45'  to  the  plane  of  the  ecliptic. 

Fig.  52- 


The  sun-spots  are  confined  in  the  main  to  two  zones, 
situated  on  each  side  of  the  equator.  They  are  seldom 
observed  elsewhere  on  the  sun's  disc. 

93.  The  Appearances  of  the  Spots. — We  have  already 
learned  from  the  spots  on  the  sun  the  direction  and  du- 
ration of  his  rotation,  and  the  inclination  of  his  axis  to 
the  plane  of  the  ecliptic.  We  will  now  study  the  appear- 
ance of  these  curious  phenomena  more  minutely.  Fig- 
ure 53  represents  a  series  of  sun-spots.  It  will  be  seen 
that  the  spots  consist  almost  invariably  of  one  or  more 
dark  portions  called  umbra,  which  seem  black  when  com- 


io6 


ASTRONOMY. 


pared  with  the  luminous  parts  of  the  disc.  Around  these 
a  gray  tint  forms  what  is  named,  improperly,  the  penum- 
bra. The  majority  of  spots  are  composed  of  one  or  sev- 
eral umbrae,  enclosed  in  one  penumbra.  But  sometimes 
spots  appear  without  the  grayish  envelope,  as  also  occa- 
sionally a  penumbra  without  an  umbra. 

Fig.  53- 


The  forms  of  the  spots,  as  shown  by  the  drawings,  are 
very  varied.  The  penumbra  most  frequently  reproduces 
the  principal  contour  of  the  umbra,  and  often  presents  a 
great  variety  of  shades  when  examined  with  a  consider- 
able magnifying  power.  On  the  exterior  edges  of  the 
penumbra,  the  gray  tint  seems  generally  the  deepest ; 
either  by  the  effect  of  contrast  with  the  brilliant  portions 
that  surround  it,  or  because  in  reality  there  is  at  these 
points  a  more  decided  tint.  Figure  54  affords  a  striking 
example  of  this  aspect  of  the  penumbra. 

This  spot  presents  the  peculiarity,  not  at  all  unfre- 
quent,  of  the  division  of  the  dark  umbra  into  several 
fragments  by  luminous  bridges  spanning  it,  as  it  were, 
from  one  side  of  the  penumbra  to  the  other. 

The  umbra  itself  is  far  from  offering  a  uniform  black 
tint.  In  reality  it  always  presents  a  variety  of  shades, 


ASTRONOMY. 


107 


as  if  the  penumbra  and  umbra  were  mingled  and  their 
tints  mixed  up  in  various  proportions. 


Fie.  s 


Under  the  best  conditions  of  air  and  of  instrument,  the 
umbra  seems  to  be  pierced,  and  to  afford  a  view  of  a 
much  darker  portion  underneath.  This  darker  portion 
has  been  called  the  nucleus.  It  appears  to  be  of  the 
most  intense  blackness,  but  it  must  be  remembered  that 
the  word  black  as  applied  to  the  sun  is  only  comparative. 
Sir  J.  Herschel  has  shown  that  a  ball  of  ignited  quick- 
lime, in  the  oxyhydrogen  flame,  though  it  seems  to  give 
out  a  light  approaching  that  of  the  sun,  appears,  when  pro- 
jected on  the  sun,  as  a  black  spot. 

94.  Dimensions  of  the  Spots.  —  The  spots  sometimes 
cover  enormous  areas.  It  is  not  uncommon  to  see  one 
with  a  surface  larger  than  that  of  the  earth.  Schroter 
measured  one  whose  extent  was  four  times  the  whole 
surface  of  the  globe.  Its  diameters  were  more  than 
29,000  miles.  Sir  W.  Herschel  measured  a  spot  con- 
sisting of  two  parts,  the  diameter  of  which  was  not  less 
than  50,000  miles.  The  most  extensive  spot  measured 


io8 


ASTRONOMY. 


was  not  less  than  186,000  miles  in  its  greatest  length, 
and  its  surface  embraced  about  25,000,000,000  square 
miles. 

If  the  spots  are  deep  rents  in  the  sun's  envelope,  the 
larger  ones  must  form  gulfs,  at  the  bottom  of  which  the 
earth  might  lie  like  a  boulder  in  the  crater  of  a  volcano. 


95.  The  Form  and  Size  of  the  Spots  are  continually 
changing.  —  Not  only  are  the  sun-spots  not  permanent, 
rarely  lasting  for  many  successive  rotations,  but  their 
forms  and  dimensions  differ  from  one  rotation  to  another ; 
sometimes  even  within  a  single  day. 

Fig-  55,  £•     (An  enlarged  view  of  the  group  A,  in  Fig.  55,  a.) 


The  modifications  which  spots  undergo  in   the  course 
of  a  rotation  are  illustrated  by  Figure  55.     These  differ- 


ASTRONOMY.  109 

ent  groups,  though  easily  recognized  again,  are  consider- 
ably changed  in  general  outline,  and  still  more  in  detail. 

These  changes  indicate  two  phenomena  going  on  simul- 
taneously, which  may  be  best  studied  separately.  First, 
there  is  indicated  a  proper  motion  of  the  spots,  more  or 
less  rapid,  and  distinct  from  the  apparent  movement  pro- 
duced by  rotation. 

The  proper  motion  of  the  spots  was  investigated  in  the 
most  thorough  manner  by  Mr.  Carrington,  who  observed 
the  sun  every  fine  day  for  more  than  eight  years,  —  from 
1853  to  1861.  After  his  discoveries  there  need  be  no 
wonder  that  different  observers  have  varied  so  greatly  in 
the  time  they  have  assigned  to  the  sun's  rotation.  He 
shows  that  all  sun-spots  have  a  movement  of  their  own, 
and  that  the  rapidity  of  this  movement  varies  regularly 
with  their  distance  from  the  solar  equator.  The  spot 
near  the  equator  travels  faster  than  those  farther  from 
it,  so  that  if  we  take  an  equatorial  spot,  we  shall  say  that 
the  sun  rotates  in  about  twenty-five  days ;  while,  if  we 
take  one  situated  half  way  between  the  equator  and  the 
poles,  in  either  hemisphere,  we  shall  say  that  it  rotates 
in  about  twenty-eight  days.  These  facts  show  that  we 
are  ignorant  of  the  exact  period  of  the  sun's  rotation. 

In  the  second  place,  the  changes  in  the  form  of  the 
spots  are  no  less  remarkable.  Sometimes  a  spot  divides 
into  several  separate  nuclei ;  sometimes  many  distinct 
nuclei  reunite  into  one.  Arago  quotes  a, curious  instance 
of  a  spot  which  seemed  to  break  upon  the  surface  of  the 
sun,  in  the  same  manner  as  a  block  of  ice  thrown  upon 
the  frozen  surface  of  a  sheet  of  water  divides  into  several 
pieces  which  slide  in  all  directions. 

Diligent  observation,  moreover,  of  the  umbra  and  pe- 
numbra with  a  powerful  instrument,  shows  that  change  is 
going  on  incessantly  in  the  region  of  the  spots.  Some- 
times after  the  lapse  of  an  hour,  many  changes  in  detail 
10 


110  ASTRONOMY. 

are  noticed :  here,  a  portion  of  the  penumbra  setting 
sail  across  the  umbra;  there,  a  portion  of  the  umbra 
melting  from  sight ;  in  another  place,  an  evident  change 
of  position  and  direction  in  masses  which  retain  their 
form. 

96.  Faculce.  —  These  spots  are  not  the  only  exception 
to  the  uniform  brightness  of  the  sun's  surface.     Near  the 
edge  of  the  solar  disc,  and  especially  about  spots  approach- 
ing the  edge,  it  is  quite  easy,  even  with  a  small  telescope, 
to  discern  certain  very  bright  streaks  of  diversified  form, 
quite   distinct  in   outline,   and  either  entirely  separate  or 
coalescing   in    various    ways   into    ridges    and    net-work. 
These  appearances,   which  have  been   called  facula,  are 
the  most  brilliant  part  of  the  sun.     Where  near  the  limb 
the  spots  become  invisible,  undulated  shining  ridges  still 
indicate   their  place.      Faculae  vary  much  in  magnitude. 
Professor  Phillips  has  observed  them  from  barely  discern- 
ible,  faintly-gleaming,  narrow  tracts,    1,000  miles  long,  to 
continuous,  complicated,  and  heavy  ridges,  40,000  miles 
and  more  in  length,  and   1,000  to  4,000  miles  broad. 

Ridges  of  this  kind  often  surround  a  spot,  and  here 
appear  more  conspicuous ;  but  sometimes  there  appears 
a  very  broad  platform  round  the  spot,  and  from  this  the 
white  crumpled  ridges  extend  in  various  directions. 

There  would  appear  to  be  a  close  connection  between 
spots  and  faculae.  An  eminent  French  observer  holds 
that  spots  are  distributed  for  the  most  part  in  groups, 
with  their  greatest  length  parallel  to  the  sun's  equator, 
and  that  the  first  spot  of  the  group  is  the  blackest,  the 
most  regular,  and  lasts  the  longest.  As  the  spots  in  the 
wake  of  the  first  disappear,  they  give  place  to  faculae, 
which  cover  the  region  where  the  spots  showed  them- 
selves ;  then  the  original  spot  appears  followed  by  a  train 
of  faculae. 

97.  "Pores,"    "Willow-Leaves?    or    "Granules:'  —  The 


ASTRONOMY.  Ill 

whole  surface  of  the  sun,  except  those  portions  occupied 
by  the  spots,  is  coarsely  mottled.  When  examined  with  a 
large  instrument  it  is  seen  that  the  surface  is  made  up 
principally  of  luminous  masses  imperfectly  separated  from 
each  other  by  rows  of  minute  dark  dots  called  pores. 
Mr.  Nasmyth  has  recently  announced  his  discovery  that 
these  pores  are  the  "polygonal  interstices  between  cer- 
tain luminous  objects  of  an  exceedingly  definite  shape 
and  general  uniformity  of  size,  which  is  that  of  the  ob- 
long leaf  of  the  willow-tree."  According  to  other  observ- 
ers, however,  these  luminous  masses  present  almost  every 
variety  of  irregular  form  ;  they  are  "  rice  grains,"  gran- 
ules or  granulations,  "  untidy  circular  masses,"  "  things 
twice  as  long  as  broad,"  and  so  on. 

Mr.  Dawes  asserts,  indeed,  that  he  has  seen  some 
nearly  in  contact  differ  so  greatly  in  size  that  one  was 
four  or  five  times  as  large  as  another ;  and  while,  in  a 
remarkably  bright  mass,  one  somewhat  resembled  a  blunt 
and  ill-shaped  arrow-head,  another,  very  much  smaller, 
and  within  5"  of  it,  was  an  irregular  trapezium  with 
rounded  corners. 

The  occasional  "  willow  F's' s6' 

leaf"  appearance  of  the 
penumbra  is  shown  in 
Figure  56. 

98.  Appearances  about 
the  Sun  during  a  Total 
Eclipse.  —  Some  minutes 
before  and  after,  but  es- 
pecially during  the  total- 
ity of  an  eclipse  of  the  sun, 
a  luminous  appearance  in 

the  form  of  a  halo  surrounds  his  disc,  and  throws  in  every 
direction  rays  of  light  separated  by  dark  spaces.  In 
many  total  eclipses,  independently  of  the  regular  corona 


112  ASTRONOMY. 

(as  this  halo  is  called),  other  light  portions  have  been 
noticed  irregularly  situated  on  the  sun's  contour.  The 
color  of  the  corona  which  immediately  surrounds  the  dark 
disc  is  sometimes  of  a  pearly  or  silvery  white,  sometimes 
yellowish,  and  even  red. 

The  explanation  generally  given  of  this  corona  is,  that 
it  indicates  the  presence  of  a  solar  atmosphere,  envel- 
oping the  radiant  body  to  an  enormous  distance. 

During  the  total  eclipse  of  1842  prominences  of  vari- 
ous f6rms  and  of  a  reddish  color  were  visible  throughout 
the  contour  of  the  moon's  limb,  during  the  period  of  to- 
tality. Some  took  the  form  of  mountain  peaks ;  others 
rose  vertically  from  the  sun's  disc,  and  then  turned  at 
right  angles;  others,  again,  appeared  completely  de- 
tached, like  floating  clouds.  Their  tint  was  sometimes 
of  a  bright  red,  sometimes  rosy,  here  and  there  variedly 
greenish-blue.  These  rose-colored  flames  or  prominences 
had  been  noticed  as  early  as  1733,  but  special  attention 
was  not  given  to  them  till  1842.  Since  then  they  have 
been  observed  with  great  care. 

It  has  now  been  proved  beyond  all  question  that  these 
protuberances  belong  to  the  sun.  In  the  observations  of 
the  total  eclipse  of  July,  1860,  it  was  seen  that  as  soon 
as  the  last  delicate  line  of  light  disappeared  behind  the 
eastern  edge  of  the  moon,  the  rose-colored  prominences 
were  seen  on  those  borders  where  the  solar  crescent  had 
just  disappeared.  On  the  opposite  side  they  were  not 
yet  entirely  visible ;  their  tops  extended  beyond  the  ob- 
scure disc  only  at  its  upper  and  lower  parts.  The  moon's 
advance  hid  by  degrees  the  prominences  first  observed, 
and  exposed  to  view,  at  the  opposite  side,  those  previ- 
ously covered. 

In  July,  1860,  the  heliograph  of  the  Kew  Observatory 
was  carried  to  Spain,  and  photographs  of  the  sun  were 
taken  at  intervals  during  the  eclipse.  These  photographs 


ASTRONOMY.  113 

showed  that  the  form  of  these  protuberances  does  not 
change  during  the  moon's  passage  across  the  sun's  disc. 
Similar  photographs  were  taken  at  Rome  by  Father  Sec- 
chi,  and  a  comparison  of  these  with  those  taken  in  Spain 
shows  that  the  prominences  did  not  sensibly  change  their 
outline  during  the  interval  between  the  occurrence  of  the 
eclipse  at  the  two  places. 

These  facts  show  that  the  prominences  do  not  belong 
to  the  lunar  disc,  and  are  not  optical  effects  produced  by 
its  presence,  but  that  they  are  absolutely  parts  of  the 
sun  itself. 

They  were  first  supposed  to  be  enormous  mountains 
on  the  surface  of  the  sun.  But  the  forms  of  many  of 
them,  and  their  occasional  complete  separation  from  the 
solar  disc,  contradict  this  hypothesis.  All  the  observed 
facts  lead  to  the  conclusion  that  these  immense  appen- 
dages, rising  25,000  and  even  50,000  miles  in  height  and 
length,  are  clouds  floating  in  the  solar  atmosphere,  whose 
presence  is  indicated  by  the  corona. 

THE   NATURE   OF   SUN-SPOTS. 

99.  Wilson's  Observations.  —  In  1769  Professor  Wilson 
of  Glasgow  watched  a  large  spot  as  it  passed  across  the 
sun's  disc.  He  first  saw  it  as  it  was  passing  towards  the 
western  limb.  At  first  the  penumbra  was  seen  entirely 
to  surround  the  umbra.  As  the  spot  approached  the 
limb,  the  penumbra  on  the  side  nearest  the  sun's  centre 
became  narrower  and  narrower,  until  it  finally  disap- 
peared, and  the  umbra  also  began  to  disappear  on  this 
side.  On  the  reappearance  of  the  spot  on  the  eastern 
limb,  the  penumbra  reappeared  on  the  eastern  side  of 
the  umbra,  but  had  vanished  on  the  western.  As  the 
spot  approached  the  sun's  centre,  the  penumbra  again 
became  visible  on  the  western  side,  as  a  narrow  line 
10* 


114  ASTRONOMY. 

which  grew  broader  and  broader  till  the  spot  reached 
the  centre  of  the  disc,  when  the  breadth  of  the  penum- 
bra was  equal  on  all  sides  of  the  umbra.  These  appear- 
ances led  Professor  Wilson  to  suppose  that  the  body  of 
the  sun  is  surrounded  by  a  luminous  envelope  of  the 
consistency  of  a  very  dense  fog,  from  which  emanate 
all  the  solar  light  and  heat,  and  that  the  spots  are  vast 
cavities  or  rents  in  this  luminous  envelope,  through  the 
bottom  of  which  the  dark  body  of  the  sun  becomes  visi- 
ble, the  shelving  sides  of  the  cavity  giving  rise  to  the 
penumbra.  When  a  spot  is  near  the  centre  of  the  sun 
the  shelving  sides  of  the  cavity  should  appear  on  all 
sides  of  the  darker  bottom ;  that  is,  the  umbra  should  be 
surrounded  on  all  sides  equally  by  the  penumbra.  When 
the  spot  is  near  either,  limb,  the  shelving  side  of  the 
cavity  should  disappear  on  the  side  towards  the  observer, 
that  is,  on  the  side  next  the  sun's  centre,  and  there  should 
be  a  penumbra  only  on  the  side  of  the  umbra  next  the 
sun's  limb.  (Compare  Figure  49.) 

100.  HerscheCs  Theory,  —  Herschel  supposed  that  the 
sun  is  surrounded  by  an  outer  or  luminous  envelope, 
and  an  inner  non-luminous  envelope,  somewhat  like  the 
stratum  of  clouds  that  surrounds  our  earth.  The  body 
of  the  sun  itself  he  supposed  to  be  dark  in  comparison 
with  the  luminous  envelope,  and  the  non-luminous  en- 
velope to  be  capable  of  reflecting  the  light  of  the  lu- 
minous envelope  about  it.  A  spot  he  supposed  to  be 
caused  by  a  rent  in  one  or  both  of  these  envelopes.  If 
only  the  outer  envelope  was  rent,  then  the  spot  would 
be  wholly  penumbra  without  any  nucleus,  since  the  non- 
luminous  envelope  would  reflect  the  light  which  fell  upon 
it  from  the  outer  envelope.  If  both  envelopes  were  rent, 
then  the  spot  would  have  a  nucleus,  since  the  dark  body 
of  the  sun  would  be  revealed.  If  the  opening  in  the 
non-luminous  envelope  were  smaller  than  that  in  the  lu- 


ASTRONOMY.  115 

minous  envelope,  as  is  usually  the  case,  the  spot  would 
appear  with  a  black  nucleus  surrounded  by  a  penumbra. 
On  this  theory,  as  on  Wilson's,  the  spots  are  cavities  in 
the  sun's  luminous  atmosphere. 

101.  Recent  Investigations  on  the  Nature  of  Sun-spots. — 
A  very  important  and  elaborate  series  of  researches  on 
the  nature  of  the  sun-spots  has  been  recently  begun  by 
Warren  De  La  Rue,  President  of  the  Royal  Astronomi- 
cal Society,  and  Balfour  Stewart  and  Benjamin  Loewy  of 
the  Kew  Observatory. 

These  investigators  have  in  their  hands  all  the  original 
drawings  of  sun-spots  executed  by  Carrington  between 
the  years  1853  and  1861,  the  collection  of  drawings  of 
the  sun  made  by  Schwabe  during  a  course  of  about  forty 
years,  and  the  photographs  of  the  sun  taken  by  the  Kew 
heliograph.  A  few  pictures  were  taken  by  this  instru- 
ment as  early  as  1858,  and  since  February,  1862,  it  has 
been  used  in  continuous  observations. 

These  investigators  have  already  arrived  at  several  im- 
portant conclusions. 

An  elaborate  examination  of  the  drawings  and  photo- 
graphs of  the  sun's  spots  has  sustained  Wilson's  con- 
clusion that  the  umbra  of  a  sun-spot  is  at  a  lower  level 
than  the  penumbra. 

The  faculae  are  regarded  as  portions  of  the  sun's  pho- 
tosphere raised  above  the  general  surface.  The  fact  that 
the  faculas  are  more  conspicuous  near  the.  edge  of  the 
sun's  disc  than  at  the  centre  supports  this  conclusion. 
For  there  is  good  reason  to  suppose  that  the  sun  is  sur- 
rounded by  an  atmosphere,  and  the  absorption  of  light 
by  this  atmosphere  would  be  much  greater  near  the  edge 
than  at  the  centre;  since  the  light  reaching  us  has  to 
travel  through  a  much  greater  extent  of  atmosphere.  If, 
then,  the  photosphere  near  the  borders  should  be  thrown 
up  to  a  great  elevation,  the  light  coming  from  it  will  es- 


Il6  ASTRONOMY. 

cape  much  of  this  atmosphere.  On  the  other  hand,  very 
little  will  be  gained  in  this  way,  when  the  elevation  is 
near  the  centre  of  the  disc,  where  the  atmospheric  ab- 
sorption is  small.  The  stereoscopic  pictures  of  the  sun 
that  have  been  obtained  also  show  some  of  the  faculae 
as  ridges. 

It  is  found,  also,  that  the  faculae  often  retain  the  same 
appearance  for  many  days  together,  as  if  the  matter  of 
which  they  are  composed  were  capable  of  remaining  sus- 
pended for  some  time.  This  permanence  of  form  would 
seem  to  show  that  the  faculae  cannot  be  elevations  of  the 
nature  of  waves  in  a  liquid  ocean  resting  on  the  surface 
of  the  sun,  but  that  they  are  rather  of  the  nature  of  a 
cloud ;  that  is,  of  solid  or  liquid  matter  formed  from  the 
condensation  of  vapor,  either  slowly  sinking  or  suspended 
in  equilibrium  in  a  gaseous  medium.  Kirchoff  has  shown 
by  means  of  the  spectroscope  that  there  exist  in  the  at- 
mosphere of  the  sun  vapors  of  such  substances  as  iron, 
which  are  condensed  into  liquids  or  solids  at  a  com- 
paratively high  temperature.  It  would  be  natural,  then, 
that  such  vapors  should  be  condensed  and  should  float 
in  the  sun's  atmosphere,  as  aqueous  vapor  is  condensed 
and  floats  in  the  form  of  clouds  in  our  atmosphere.  The 
portion  of  the  sun,  then,  which  appears  luminous  to  us, 
is  probably  a  condensed  stratum  of  those  vapors  which 
exist  in  the  sun's  atmosphere,  and  which  are  capable  of 
condensation  at  a  high  temperature. 

A  comparison  of  a  large  number  of  spots  shows  that 
faculae  are,  on  an  average,  to  the  left  of  their  accompany- 
ing spots.  From  the  way  in  which  the  spots  often  break 
up,  and  from  the  fact  that  detached  portions  of  lumi- 
nous matter  often  appear  to  float  across  the  spot  without 
producing  any  permanent  alteration,  these  observers  are 
disposed  to  think  that  the  umbra  and  penumbra  of  a 
spot  both  lie  beneath  the  sun's  photosphere. 


ASTRONOMY.  1  I  7 

They  conclude  that  the  spots  are  produced  by  the 
cooling  of  the  sun's  photosphere,  and  they  believe  that 
this  cooling  is  occasioned  by  downward  currents  in  the 
solar  atmosphere  which  bring  the  cooler  atmosphere  of 
the  higher  regions  down  into  that  of  the  photosphere. 
The  supposition  that  the  spots  are  produced  by  the  cool- 
ing effects  of  downward  currents  is  supported  by  the 
proper  motion  of  the  spots.  It  will  be  remembered  that 
the  spots  have  all  a  proper  motion  in  the  direction  of 
the  sun's  rotation,  and  of  greater  rapidity  in  proportion 
as  they  are  nearer  the  equator.  Now  if  they  are  pro- 
duced by  downward  currents,  the  air  in  the  upper  re- 
gions must  have  a  greater  velocity  than  that  in  the  lower 
regions,  and  it  must  consequently  tend  to  increase  the 
velocity  of  this  lower  air,  which  would  tend  to  give  the 
spots  a  proper  motion  in  the  direction  of  the  sun's  rota- 
tion. This  velocity  in  the  upper  regions  would  be  great- 
est at  the  equator,  hence  the  proper  motion  of  the  spots 
should  be  greatest  there. 

But  these  downward  currents  should  be  accompanied 
with  upward  currents.  There  should  then  be  faculae  in 
the  neighborhood  of  the  spots.  And  as  the  air  in  the 
lower  regions  has  less  velocity  than  that  in  the  upper  re- 
gions, the  faculae  should  fall  behind  the  spots.  This  is 
exactly  confirmed  by  observation. 

This  theory  of  the  nature  and  cause  of  the  sun-spots 
is  certainly  simpler  and  more  satisfactory  than  that  framed 
by  Herschel. 

The  same  observers  have  measured  the  area  of  the  sun- 
spots  on  Carrington's  drawings  and  on  the  photographs 
of  the  sun.  They  have  thus  discovered  that  the  maxi- 
mum area  of  visible  spots  is  always  on  the  part  of  the 
sun's  disc  which  is  opposite  the  planet  Venus.  When 
Venus  is  at  superior  conjunction,  the  spots  attain  the 
greatest  area  where  they  cross  a  line  drawn  through  the 


Il8    '  ASTRONOMY. 

centre  of  the  sun's  disc  perpendicular  to  the  plane  of  the 
ecliptic.  As  Venus  passes  on  from  superior  conjunction, 
the  spots  attain  their  greatest  area  to  the  right  of  this 
central  line. 

They  have  found,  too,  that  when  Venus  is  at  or  near 
the  plane  of  the  sun's  equator,  the  belts  of  spots  ap- 
proach the  sun's  equator ;  and  that  when  Venus  is  most 
distant  from  that  plane,  they  recede  from  the  equator. 
The  planet  Venus,  then,  has  a  remarkable  influence  on 
the  size  and  position  of  the  sun's  spots.  They  have  also 
found  that  the  area  of  the  spots  on  crossing  the  central 
line  on  the  sun's  disc  is  much  greater  when  Venus  and 
Jupiter  are  both  on  the  opposite  side  of  the  sun  from  the 
earth,  than  when  Venus  is  on  the  opposite  side  and  Ju- 
piter on  the  same  side  as  the  earth.  This  shows  that 
the  planet  Jupiter  has  also  considerable  influence  on  the 
sun's  spots. 

SUMMARY. 

Place  the  centre  of  the  sun  at  the  centre  of  the  earth, 
and  his  circumference  would  extend  far  beyond  the  moon's 
orbit.  (87.) 

The  sun's  disc  is  seldom  free  from  dark  patches.  These 
patches  are  called  sun-spots. 

Sun-spots  appear  in  greatest  numbers  at  intervals  of 
about  twelve  years.  (88.) 

These  spots  belong  to  the  disc  of  the  sun.     (90.) 

The  rotation  of  the  sun  on  his  axis,  and  the  inclination 
of  his  axis  to  the  plane  of  the  ecliptic,  have  been  ascer- 
tained by  means  of  the  sun-spots.  (91,  92.) 

The  spots  have  usually  an  umbra  and  a  penumbra. 
The  umbra  is  not  uniformly  dark.  (93.) 

The  spots  sometimes  cover  enormous  areas.     (94.) 

The  spots  have  a  proper  motion   in   the  direction   cf 


ASTRONOMY.  119 

the  sun's  rotation.  Those  near  the  equator  move  much 
faster  than  those  away  from  it.  They  are  also  constantly 
changing  their  form.  (95.) 

Facula  are  bright  streaks  on  the  sun's  disg.  They 
seem  to  be  connected  with  the  spots.  They  usually  ap- 
pear in  the  rear  of  these.  (96.) 

The  general  disc  of  the  sun  is  coarsely  mottled.  "Wil- 
low leaves"  are  sometimes  seen  about  the  spots.  (97.) 

During  a  total  eclipse  the  sun  is  surrounded  by  a 
corona,  and  by  rose-colored  clouds.  (98.) 

Professor  Wilson  supposed  that  the  spots  are  vast 
rents  in  the  sun's  luminous  atmosphere,  through  which 
the  dark  body  of  the  sun  is  visible.  (99.) 

According  to  Herschel's  theory  the  sun  is  surrounded 
by  two  envelopes,  the  outer  one  luminous,  and  the  inner 
one  non-luminous.  When  both  envelopes  are  rent,  and 
the  opening  in  the  outer  envelope  is  larger  than  that  in 
the  inner,  the  spot  has  both  an  umbra  and  a  penumbra. 
(100.) 

An  important  investigation  of  the  nature  of  the  sun- 
spots  has  been  recently  begun  by  De  La  Rue,  Stewart, 
and  Loewy. 

They  regard  the  sun's  photosphere  as  of  the  nature  of 
a  cloud,  and  the  faculae  as  portions  of  this  cloud  raised 
above  the  general  surface.  They  find  that  the  faculae 
are  more  often  to  the  left  of  the  spots  than  elsewhere. 
They  have  decided  that  both  the  umbra  and  penumbra 
are  beneath  the  sun's  photosphere. 

They  think  the  spots  are  produced  by  the  cooling  of 
the  sun's  photosphere  by  downward  currents.  They 
have  shown  that  Venus  and  Jupiter  have  a  marked  influ- 
ence on  the  sun-spots.  (101.) 


120  ASTRONOMY. 


MERCURY. 

102.  Ifs  Distance  from  the  Sun,  Period  of  Revolution,  etc. 
—  Mercury,  as  we  have   seen,  is  the  planet  nearest  the 
sun.     Its  greatest  elongation  from  the  sun  is  about  29°  ; 
hence  it  is  never  seen  at  a  great  distance  from  the  hori- 
zon, or  long  after  sunset  or  before  sunrise.     And  as  the 
atmosphere  near  the  horizon  is  usually  charged  with  va- 
pors, Mercury  is  seldom  a  very  conspicuous  object. 

The  mean  distance  of  this  planet  from  the  sun  is 
37,000,000  miles,  and  its  period  of  revolution  is  about 
three  months.  Its  orbit  is  a  very  flat  ellipse,  so  that  its 
distance  from  the  sun  varies  greatly.  At  perihelion  it  is 
less  than  30,000,000  miles  from  the  sun,  while  at  aphe- 
lion it  is  more  than  44,000,000  miles  from  him.  Its  dis- 
tance from  the  sun,  then,  varies  by  about  15,000,000 
miles.  Its  orbit  is  inclined  to  the  ecliptic  about  7°, 
which  is  more  than  that  of  any  other  of  the  larger  plan- 
ets. 

If  its  inferior  conjunction  occurs  when  it  is  near  one 
of  its  nodes  (67),  it  will  be  seen  to  cross  the  sun.  It 
then  appears  as  a  black  circular  disc  projected  upon  the 
sun.  Accurate  measurements  taken  at  a  large  number 
of  observations  of  these  transits  of  -Mercury  show  that 
the  disc  is  always  an  exact  circle.  Hence  we  conclude 
that  Mercury  is  an  exact  sphere. 

103.  Its  Distance  from  the  Ecfrth,   its  Diameter,   etc.  — 
Since  the  orbit  of  Mercury  lies  inside  of  the  orbit  of  the 
earth,    its    distance   from    our   planet    must   vary   greatly. 
At  inferior  conjunction  it  is  nearer  the  earth  by  the  whole 
diameter  of  its  orbit  than  it  is  at  superior  conjunction. 
Hence  it  appears  much  larger  at  the  former  time  than 
at  the  latter.     Its  angular  diameter  varies  from  5"  to  12". 
Knowing  this  angular  diameter,  and  the  distance  of  the 


ASTRONOMY.  I  2  I 

planet  from  the  earth,  we  can  readily  compute  its  diam- 
eter in  miles  by  the  method  already  used  in  the  case  of 
the  sun  (87).  Its  diameter  is  thus  found  to  be  about 
3,000  miles. 

When  examined  with   a   telescope  this  planet  presents 
phases  exactly  like  those  of  the  moon.     Figure  57  shows 

Fig.  57- 


these  phases,  and  also  the  comparative  size  of  the  planet 
as  seen  in  different  parts  of  its  orbit.  It  appears  at  first 
as  a  luminous  disc,  nearly  circular,  which  by  degrees  is 
reduced  on  the  side  towards  the  east,  until  not  more 
than  half  a  circle  is  visible  at  the  time  of  its  greatest 
elongation  from  the  sun ;  it  then  becomes  a  crescent, 
which  grows  narrower  and  narrower,  until  just  before  in- 
ferior conjunction  it  is  visible  only  as  a  fine  luminous 
thread.  It  repeats  these  phases  in  the  opposite  order 
when  it  reappears  on  the  other  side  of  the  sun. 

1 04.  The  Explanation  of  these  Phases.  —  These  phases 
prove  that  Mercury  is  not  self-luminous,  but  shines  by 
reflected  sunlight.  One  half  of  the  planet  is  of  course 
always  illuminated  by  the  sun,  and  it  is  evident  that  at 
superior  conjunction  this  illuminated  half  is  turned  to- 
wards the  earth,  so  that  its  whole  disc  then  appears  lu- 
minous. At  inferior  conjunction  it  is  equally  evident 
that  the  illumined  half  is  turned  away  from  the  earth  ; 
since  it  will  always  be  turned  toward  the  sun.  At  its 
ii 


122  ASTRONOMY. 

greatest  elongation  half  of  the  illumined  hemisphere  will 
be  turned  towards  the  earth,  and  the  illumined  disc  will 
then  appear  as  a  semicircle.  Between  the  greatest  elon- 
gation and  superior  conjunction  more  than  half  of  the 
illumined  hemisphere  is  turned  toward  the  earth ;  while 
between  the  elongation  and  inferior  conjunction  less  than 
half  of  the  illumined  hemisphere  is  turned  towards  us. 

105.  Mercury's  Period  of  Rotation.  —  The  great  prox- 
imity of  Mercury  to  the  sun  renders  the  observation  of 
this  planet  somewhat  difficult,  so  that  very  little  is  known 
of  its  surface.  The  German  astronomer  Schroter,  who 
observed  Mercury  very  carefully  in  the  latter  part  of  the 
last  century,  considered  that  he  had  decided  evidence  of 
the  existence  of  high  mountains  on  the  planet ;  and  by 
watching  these  he  came  to  the  conclusion  that  Mercury 
rotates  on  its  axis  in  a  little  over  twenty-four  hours. 

Schroter  observed  that  during  the  crescent  phase  of 
the  planet  the  line  which  separated  the  illumined  from 
the  dark  portion  of  the  disc  appeared  somewhat  jagged, 
as  shown  in  Figure  58.  These  markings  evidently  indi- 


cate the  existence  of  high  mountains,  which  intercept  the 
sunlight,  and  of  valleys  plunged  in  the  shade,  which  lie 
near  the  parts  of  the  surface  of  the  planet  then  illumined. 
These  markings  are  not  always  visible,  but  appear  and 


ASTRONOMY.  123 

disappear  at  intervals ;  and  it  was  from  these  intervals 
that  Schroter  determined  the  rotation  of  the  planet.  But 
as  he  is  the  only  astronomer  who  has  been  able  to  make 
out  these  irregularities  on  the  disc  of  Mercury,  the  pe- 
riod of  rotation  must  be  considered  as  still  very  un- 
certain. 

1 06.  The  Inclination  of  its  Orbit,  and  its  Seasons.  - 
Schroter  observed  some  dark  bands  on  the  disc  of  Mer- 
cury, which  he  considered  as  an  equatorial  zone.  It  was 
from  the  direction  of  these  bands  that  he  deduced  the 
inclination  of  the  axis  of  rotation  to  the  plane  of  the 
planet's  orbit.  This  he  estimated  at  about  20°,  which 
would  make  the  equator  of  Mercury  inclined  to  the  plane 
of  the  orbit  at  an  angle  of  about  70°.  It  will  be  seen 
that  this  inclination  is  about  three  times  as  great  as  that 
of  the  earth's  equator  to  the  plane  of  the  earth's  orbit,  or 
the  ecliptic.  This  inclination,  together  with  the  great 
variation  of  Mercury's  distance  from  the  sun,  would  give 
a  remarkable  variety  of  seasons,  with  great  extremes  of 
heat  and  cold. 

Figure  59  shows,  according  to  Schroter,  the  angle  at 
which  Mercury  presents  himself  to  the  sun  at  the  com- 
mencement of  each  season.  It  will  be  seen  that  very 
extensive  zones  about  the  poles  enjoy  at  one  season, 
during  the  summer,  continuous  day ;  while  at  another, 
during  their  winter,  they  are  plunged  in  profound  dark- 
ness. It  is  only  during  a  short  period,  and  near  the 
planet's  equinoxes,  that  these  zones  see  light  and  dark- 
ness succeed  one  another  in  the  same  day. 

These  polar  zones  are  of  course  much  broader  than 
the  corresponding  zones  on  the  earth. 

Since  the  light  and  heat  which  a  planet  receives  from 
the  sun  diminish  as  the  square  of  the  distance  increases, 
it  follows  that  the  intensity  of  the  sunlight  at  Mercury  is 
about  seven  times  as  great  as  at  the  earth. 


124 


ASTRONOMY. 

Fig.  59- 


It  will  be  noticed  in  Figure  58  that  the  illumined  part 
of  the  disc  shades  off  gradually  into  the  dark  part.  This 
gradual  shading  off  indicates  the  presence  of  an  atmos- 
phere about  Mercury,  the  darkish  part  being  the  zone  of 
twilight  which  separates  the  full  light  of  day  from  the 
darkness  of  night  This  zone  of  twilight,  as  at  the  earth, 
must  be  caused  by  an  atmosphere. 


VENUS. 

107.  Its  Distance  from  the  Sun,  Time  of  Revolution,  Di- 
ameter, etc.  —  The  second  planet  from  the  sun  is  Venus. 
Her  mean  distance  (48)  is  69,000,000  miles,  and  her 
period  of  revolution  about  yj  months. 

While  the  orbit  of  Mercury  differs  more  from  a  circle 
than  that  of  any  other  planet,  the  orbit  of  Venus  is  found 
to  be  nearer  a  circle  than  that  of  any  other  planet. 
Hence  she  is  but  little  nearer  the  sun  at  perihelion  than 
at  aphelion.  Her  orbit  is  inclined  to  the  ecliptic  at  an 


ASTRONOMY.  125 

angle  of  3°  23'.  When  examined  with  a  telescope  she 
presents  phases  like  those  of  Mercury ;  proving  that  she 
is  not  self-luminous,  but  shines  with  light  borrowed  from 
the  sun. 

The  distance  of  Venus  from  the  earth  varies  more  than 
that  of  Mercury,  since  the  diameter  of  her  orbit  is  greater 
than  his.  At  inferior  conjunction  Venus  is  of  course 
about  138,000,000  miles  nearer  the  earth  than  at  superior 
conjunction.  Hence  the  apparent  diameter  of  the  planet 
varies  greatly,  ranging  from  70"  to  less  than  10".  The 
actual  diameter  of  Venus  is  about  7,800  miles,  or  a  little 
less  than  that  of  the  earth. 

Figure  60  shows  the  apparent  size  of  Venus  at  its 
greatest,  its  mean,  and  its  least  distance  from  the  earth. 


Venus  appears  as  an  evening  star  for  a  period  of  about 
9|-  months,  and  is  then  a  morning  star  for  the  same  length 
of  time. 

1 08.  Time  of  Rotation,  Inclination  of  Axis,  etc. — Venus 
is  the  most  conspicuous  of  all  the  planets.  Her  light  is 
often  brilliant  enough  to  cast  a  shadow,  and  she  is  some- 
times visible  at  midday.  Her  greatest  brilliancy  is  not 
near  her  inferior  conjunction,  since  the  illumined  portion 
of  her  disc  is  then  reduced  to  a  mere  thread  of  light. 
It  occurs  at  an  elongation  of  about  40°,  and  her  phase  is 
ii  * 


126  ASTRONOMY. 

then  about  the  same  as  that  of  the  moon  three  days  from 
new  moon. 

The  brilliancy  of  Venus  is  so  great  as  to  render  accu- 
rate observation  of  her  disc  almost  impossible.  We  do 
not  know  whether  she  is  flattened  at  the  poles,  like  the 
earth,  or  not. 

The  terminator  of  Venus  (the  line  dividing  the  illu- 
mined from  the  dark  part  of  the  disc),  as  seen  at  times 
by  Schroter,  presented  considerable  Irregularity  of  out- 
line. This  irregularity,  as  in  the  case  of  Mercury  (105), 
indicates  the  presence  of  mountains  and  valleys.  By  ob- 
serving the  interval  between  the  disappearance  and  re- 
appearance of  certain  of  these  irregularities',  this  astron- 
omer came  to  the  conclusion  that  Venus  rotates  on  her 
axis  in  a  little  less  than  twenty-four  hours. 

Schroter  made  the  inclination  of  the  planet's  axis  to 
the  plane  of  its  orbit  about  20°,  and  several  other  ob- 
servers have  arrived  at  very  nearly  the  same  result.  The 
change  of  seasons  and  of  the  length  of  day  and  night 
would  therefore  be  about  the  same  on  Venus  as  we  have 
supposed  them  to  be  on  Mercury. 

The  gradual  shading  off  of  the  illumined  portion  of 
the  disc  of  Venus  indicates  the  existence  of  twilight  on 
this  planet,  and  consequently  of  an  atmosphere  (106). 

109.  Has  Venus  a  Satellite? — According  to  Cassini 
and  several  observers  of  the  last  century,  Venus  is  at- 
tended by  a  satellite.  But  recent  astronomers  have  not 
been  able  to  detect  it,  though  they  are  provided  with 
much  better  instruments  for  observation.  It  is,  therefore, 
now  generally  believed  that  this  planet  has  no  satellite. 

no.  Transits  of  Venus.  —  Venus,  as  we  have  already 
seen,  crosses  the  sun's  disc  whenever  her  inferior  con- 
junction happens  near  one  of  her  nodes  (67). 


ASTRONOMY.  127 


THE  ZODIACAL  LIGHT. 

in.  Its  Appearance.  —  In  the  evenings  about  the  time 
of  the  vernal  equinox,  when  in  our  latitude  the  twilight 
is  of  short  duration,  if  we  examine  the  horizon  towards 
the  west  soon  after  sunset,  we  may  see  a  faint  light  that 
rises  in  a  triangular  form  among  the  constellations. 

This  appearance  is  known  as  the  Zodiacal  Light.  Those 
not  familiar  with  it  might  confound  this  glimmering  with 
the  milky  way,  or  with  the  ordinary  twilight,  or  even  with 
an  aurora.  But  with  a  little  attention  it  is  impossible  to 
mistake  it.  Its  triangular  shape,  its  elevation,  and  its 
inclination  to  the  horizon,  all  serve  to  distinguish  it. 

As  the  days  lengthen,  and  with  them  the  duration  of 
twilight,  the  zodiacal  light  becomes  invisible,  at  least  in 
our  latitude.  But  it  may  be  again  seen  before  sunrise 
in  the  east,  about  the  time  of  the  autumnal  equinox,  in 
September  and  October,  when  the  morning  twilight  is 
short.  At  places  favorably  situated,  even  in  the  temper- 
ate zone,  the  zodiacal  light  can  be  seen  at  almost  every 
season  of  the  year. 

In  our  climate,  the  light  of  the  zodiacal  light  is  rather 
more  intense  than  that  of  the  Milky  Way,  and  much 
more  uniform. 

If  now  we  pass  from  the  temperate  zone  of  either  hemi- 
sphere towards  the  tropical  zone,  the  zodiacal  light  in- 
creases in  intensity  and  height ;  and  it  can  be  observed 
throughout  the  year. 

112.  Its  Cause. — The  most  probable  of  the  many  ex- 
planations that  have  been  given  of  the  zodiacal  light  is 
that  it  is  a  flattened  nebulous  body  surrounding  the  sun 
at  some  distance.  The  direction  of  the  axis  of  the  cone 
of  light,  if  prolonged  below  the  horizon,  always  passes 
through  the  sun,  as  shown  in  Figure  61. 


128 


ASTRONOMY. 
Ficr.  6 1. 


It  was  believed  at  first  that  this  direction  coincided 
with  the  solar  equator,  but  it  has  been  found  to  coincide 
more  nearly  with  the  plane  of  the  earth's  orbit,  or  the 
ecliptic. 

The  distance  from  the  summit  of  the  cone  to  the  mid- 
dle of  its  base  at  the  horizon  varies  with  the  time  of 
observation.  This  ring  sometimes  extends  as  far  as  the 
earth's  orbit,  and  even  beyond  it ;  at  other  times  it  is  en- 
closed within  this  orbit.  This  may  be  explained  by  sup- 
posing either  that  the  form  of  the  ring  is  oval,  or  that  it 
is  circular  and  that  the  sun  does  not  lie  in  its  centre. 

Some  suppose  that  the  zodiacal  light  is  formed  of 
myriads  of  solid  particles  analogous  to  aerolites,  having 
a  common  general  movement,  but  travelling  separately 
•about  the / sun  as  a  centre.  The  light  of  the  ring  would 
thus  be  produced  by  the  accumulation  of  this  multitude 
of  brilliant  points,  reflecting  towards  us  the  light  borrowed 
by  each  of  them  from  the  sun.  Others  regard  it  as  a 


ASTRONOMY.  1 29 

ring  of  thin  nebulous  matter  much  like  the  train  of  com- 
ets; others  as  a  vaporous  ring  which  surrounds  the  earth 
at  some  distance. 


THE    EARTH. 

113.  The  third  planet  in  the   order   of  distance  from 
the  sun  is  the  earth.     We  have  already  found  its  mean 
distance  from   the    sun  to   be   95,000,000  miles;  that   it 
revolves  about  the  sun  in  an  ellipse,  in  a  period  of  one 
year ;  that  it  rotates  on  its  axis  in  a  little  less  than  twenty- 
four  hours;  that  this  axis  is  inclined  to  the  plane  of  its 
orbit  by  an  angle  of  66J° ;  that  this  inclination  gives  rise 
to  the  change  of  seasons  and  the  varying  length  of  day 
and  night ;  that  the,  mean  diameter  of  our  planet  is  about 
8,000  miles;  and  that  it  is  not  a  perfect  sphere,  but  is 
flattened  somewhat  at  the  poles. 

The  earth  has  also  an  atmosphere  of  known  composi- 
tion, which  gives  rise  to  the  phenomena  of  twilight.  The 
land  surface  of  the  earth  is  also  jagged  with  mountains, 
as  we  have  seen  there  is  reason  to  believe  is  also  the 
case  with  the  surface  of  Mercury  and  Venus. 

The  earth  is  the  first  planet  in  order  from  the  sun  that 
is  known  to  be  accompanied  by  a  satellite.  The  earth, 
like  Mercury  and  Venus,  shines  by  reflected  light,  as 
will  be  proved  hereafter. 

THE    MOON. 

114.  Her  Distance,  Diameter,  Periodic  Time,  etc. — T]he 
mean  distance  of  the  moon,  as  we  have  seen,  is  about 
thirty  times  the  diameter  of  the  earth,  and  her  mean  an- 
gular diameter  is  about  31'.     From  this  her  real  diameter 
is  found  to  be  somewhat  more  than  2,000  miles.     The 
moon  revolves  around  the  earth  in  an  ellipse  whose  plane 

9 


130  ASTRONOMY. 

is  inclined  to  the  plane  of  the  earth's  orbit  by  an  angle 
of  about  5°.  She  performs  a  revolution  in  about  27  J 
days.  Owing,  however,  to  the 'motion  of  the  earth  in 
its  orbit,  the  synodical  revolution  of  the  moon,  or  the 
interval  between  two  successive  new  moons,  is  about  29  J 
days. 

115.  The  Phases    of  the  Moon.  — The  phases   of   the 
moon  depend  on  the  position  of  the  moon  with  respect 
to  the  sun,  or,  what  amounts  to  the  same  thing,  her  dis- 
tance from  conjunction,  which   is  termed  in  astronomical 
language  the  age  of  the  moon.     Being  an  opaque  spher- 
ical body  reflecting  the  sun's  light,   she  can  appear  fully 
illuminated  only  when  opposite  the  sun,  and  in  all  other 
positions  her  illuminated  disc  appears  less  than  a  circle. 
Soon  after  conjunction  with  the  sun  she  may  be  seen  as 
a  very  narrow  crescent,   a  little  above  the  western  hori- 
zon at   sunset;   for,  being   then   between   the   earth  and 
sun,  her  illuminated  surface  is  in  a  great  measure  turned 
from  us.     As   she   advances  in  her  orbit,  the  dark  part 
gradually  diminishes  until  the  moon  is  90°  from  conjunc- 
tion, which  is  called  the  first  quarter,  and  then  the  illu- 
mined and  unillumined  parts  are  equal.     After  this  point, 
the  illumined  surface  increases  till  the  moon  is  in  oppo- 
sition, when  she  is  said  to  be  full,  and  presents  to  us 
her  whole  enlightened  disc.     The  bright  part  then  begins 
to  diminish,  and  again  forms  one  half  of  her  surface  when 
the  moon  is  90°  from  conjunction,  or  at  the  last  quarter. 
It  then  becomes  narrower  as  she  approaches  conjunction, 
till  a  thin  crescent  above  the  eastern  horizon  shortly  be- 
fore  sunrise   is   all   that  remains.      These  phases  repeat 
themselves   after  the   interval   of   a  synodical  revolution, 
and  depend  upon  the  position  of  the  visible,  with  refer- 
ence to  the  enlightened,  hemisphere  of  the  moon. 

1 1 6.  Libration.  — The  most  casual  observer  of  the  moon 
can  hardly  have  failed  to  remark  that  she  always  presents 


ASTRONOMY.  131 

very  nearly  the  same  face  towards  us,  and  a  little  reflec- 
tion will  convince  him  that  the  cause  of  this  must  lie  in 
the  very  near  equality  of  her  periods  of  axial  rotation 
and  synodical  revolution  round  the  earth.  If  these  periods 
were  exactly  equal,  and  the  moon's  motions  exactly  uni- 
form, we  should  have  the  same  hemisphere  turned  to- 
wards us  without  the  slightest  variation.  But  the  motion 
in  her  orbit  is  subject  to  small  irregularities,  while  that 
on  her  axis  is  perfectly  uniform,  and  for  this  reason  a 
phenomenon  termed  libration  takes  place,  whereby  we 
occasionally  see  a  little  more  of  one  edge  of  the  moon 
than  usual,  either  on  the  eastern  or  western  side  of  her 
equatorial  region.  Suppose,  for  instance,  that  conjunc- 
tion occurs  when  the  moon  is  at  perigee,  or  nearest  the 
earth,  and  that  the  moon  rotates  on  its  axis  at  a  uni- 
form rate  and  once  during  a  sidereal  revolution.  But 
the  moon  moves  in  her  orbit  faster  at  perigee  than  else- 
where. She  would  accordingly  perform  the  first  quarter 
of  her  revolution  before  she  had  performed  a  quarter  of 
a  rotation.  We  should  therefore  see  a  little  more  of  her 
western  edge  than  we  should  if  she  had  performed  a 
quarter  of  her  rotation.  Again,  suppose  that  conjunc- 
tion occurs  when  the  moon  is  at  apogee,  or  farthest  from 
the  earth.  Then  while  she  is  performing  a  quarter  of  a 
revolution,  she  will  perform  more  than  a  quarter  of  a 
rotation,  and  we  should  see  more  of  her  eastern  edge 
than  we  should  if  she  had  performed  just,  a  quarter  ro- 
tation. 

This  libration,  which  is  due  to  the  moon's  unequal 
rate  of  motion  in  her  orbit,  is  usually  called  libration  in 
longitude. 

The  moon,  then,  rotates  on  her  axis  in  the  mean 
period  of  a  sidereal  revolution,  and  it  has  been  found  by 
observation  that  the  axis  of  this  rotation  is  not  quite 
perpendicular  to  the  plane  of  her  orbit.  Now  since  the 


132  ASTRONOMY. 

axis  always  maintains  the  same  direction,  it  follows  that 
we  are  enabled  at  times  to  see  a  little  more  of  the  polar 
regions  than  at  others.  This  phenomenon  is  called  //- 
bration  in  latitude. 

Since  we  are  situated  four  thousand  miles  above  the 
centre  of  the  earth,  we  see  at  the  rising  of  the  moon  a 
little  more  of  the  western  edge  than  we  should  if  we 
were  viewing  the  moon  from  the  centre  of  the  earth. 
For  the  same  reason,  we  see  at  the  setting  of  the  moon 
a  little  more  of  the  eastern  edge  of  the  moon  than  we 
should  if  we  were  situated  at  the  centre  of  the  earth. 
This  phenomenon  is  called  parallactic  libration. 

117.  The  Earth's  Phases  as  seen  from  the  Moon.  —  It 
is  a  well-known  fact  that  at  the  time  of  new  moon  the 
dark  part  of  the  moon's  surface  is  partially  illumined,  so 
that  it  becomes  visible  to  the  naked  eye.     This  must  be 
due  to  the  light  reflected  to  the  moon  from  the  earth. 
Since  at  new  moon  the  moon  is  between  the  earth  and 
sun,  it  follows  that  when  it  is  new  moon  at  the  earth,  it 
must  be  full  earth  at  the  moon.     Hence  while  the  bright 
crescent  is   enjoying   full   sunlight,    the   dark   part   of  its 
surface  is  enjoying  the  light  of  the  full  earth. 

1 1 8.  The  Apparent  Size  of  the  Moon.  —  The  apparent 
magnitude  of  the  lunar  disc  not  only  varies  with  the  dis- 
tance of -the  moon  from  the  earth,  but  even  on  the  sur- 
face of  our  globe,  and  at  the  same  instant,  the  disc  does 
not  appear  of  equal  magnitude  to  all  observers.       It  ap- 
pears  larger   to   an  observer  who   sees   the   moon  rising 
or  setting,  than  to  him  who  sees  it  at  the  zenith. 

In  Figure  62  the  distance  A  M  of  the  moon  from  an 
observer  at  A  is  seen  to  be  nearly  equal  to  its  real  dis- 
tance from  the  centre  of  the  earth,  while  at  the  same 
time  its  distance  A  M  from  an  observer  at  A  is  4,000 
miles  less  than  its  distance  from  the  centre  of  the  earth. 
Hence  the  moon  is  nearer  an  observer  at  A'  by  about 
^V  of  its  distance  than  to  an  observer  at  A. 


ASTRONOMY.  133 

Fig.  62. 


Notwithstanding  it  is  much  nearer  when  at  the  zenith 
than  at  the  horizon,  it  seems  to  us  much  larger  at  the 
horizon. 

This  is  a  pure  illusion,  as  we  become  convinced  when 
we  measure  the  disc  with  accurate  instruments,  so  as  to 
make  the  result  independent  of  our  ordinary  way  of  judg- 
ing. When  the  moon  is  near  the  horizon,  it  seems  placed 
beyond  all  the  objects  on  the  surface  of  the  earth  in  that 
direction,  and  therefore  farther  off  than  at  the  zenith, 
where  no  intervening  objects  enable  us  to  judge  of  its 
distance.  In  any  case,  an  object  which  keeps  the  same 
apparent  magnitude  seems  to  us,  through  the  instinctive 
habits  of  the  eye,  the  larger  in  proportion  as  we  judge 
it  to  be  more  distant. 

A  recent  discovery  of  very  great  interest  shows  us  that 
in  the  case  of  the  moon  the  word  apparent  means  much 
more  than  it  does  in  the  case  of  other  celestial  bodies. 
Indeed,  its  brightness  causes  our  eyes  to  'play  us  false. 
As  is  well  known,  the  crescent  of  the  new  moon  seems 
part  of  a  much  larger  sphere  than  that  which  it  has 
been  said,  time  out  of  mind,  to  "  hold  in  its  arms."  We 
now  learn  that  the  bright  portion  of  the  moon,  as  seen 
with  our  measuring  instruments,  as  well  as  when  seen  with 
the  naked  eye,  covers  a  larger  space  in  the  field  of  the 
telescope  than  it  would  if  it  were  not  so  bright.  This 


134  ASTRONOMY. 

has  been  recently  proved  by  measuring  the  dark  moon 
by  means  of  the  occultation  of  a  star.  In  this  way  the 
Astronomer  Royal  of  England  has  shown  that  the  di- 
ameter of  the  moon  hitherto  received  is  too  large  by  2". 

119.  The  Path  of  the  Moon  through  Space.  —  Since  the 
earth  is  moving  in   its  orbit  at  the   same  time  that  the 
moon  is  revolving  about  it,  it  follows  that  the  path  de- 
scribed by  the  moon  through  space  is  much  the  same  as 
that    described    by    a    point    on    the    circumference   of  a 
wheel  which  is  rolled  over  another  wheel.     If  we  place  a 
circular  disc  against  the  wall,  and  carefully  roll  along  its 
edge  another  circular  disc  to  which  a  piece  of  lead  pencil 
has  been  fastened  so  as  to  mark  upon  the  wall,  the  curve 
described  will  somewhat  resemble  that  described  by  the 
moon.     This  curve  is  called  an  epicycloid,   and  it  will  be 
seen  that  at  every  point  it  is  concave  towards  the  centre 
of  .the  larger  disc.     In  the  same  way  the  moon's  orbit  is 
at  every  point  concave  towards  the  sun. 

120.  Harvest  Moon.  —  The    full    moon    which    occurs 
nearest   to   the  autumnal  equinox   has   long   been   called 
the  Harvest  Moon,  from  the  fact  that  the   difference  be- 
tween  the   times  of  the  moon's  rising  on   two  successive 
nights  is  then  at  a   minimum,  and   the   long  duration  of 
moonlight,   thus  afforded    soon    after   sunset,   is  very  ad- 
vantageous to  the  farmer  at  this  busy  season.     This  near 
coincidence  in  the  times  of  several  successive  risings  oc- 
curs every  lunar  month,  when  the  moon  is   in  the  signs 
Pisces  and  Aries,  but  it  attracts  attention  only  when  the 
moon  is  at  the  full  in  these  signs,  and  this  can  happen 
only  in  August  or  September.     The  least  possible  differ- 
ence  between    two    successive  risings   in    the  latitude  of 
Boston    is  about  twenty-three  minutes.     When  the  moon 
is  in  Libra,  and  at  the  same  time  near  the  descending 
node  of  her  orbit,   the  difference  between   the   times    of 
rising  on  two  evenings  is  the  greatest  possible,   amount- 
ing to  about  one  hour  and  seventeen  minutes. 


ASTRONOMY.  135 

121.  The  Surface  of  the  Moon. — The  moon  is  much 
the  nearest  to  us  of  all  the  heavenly  bodies,  and  we  are 
consequently  best  acquainted  with  its  surface.  The  na- 
ked eye  readily  discerns  that  the  disc  of  the  full  moon 
is  not  uniformly  bright :  light  and  dark  regions  diversify 
it,  giving  the  idea  of  continents  and  seas  like  those  on 
our  own  globe.  In  fact,  the  earlier  selenographers  con- 
sidered the  dull,  grayish  spots  to  be  water,  and  termed 
them  the  lunar  seas,  bays,  and  lakes.  They  are  so  called 
on  lunar  maps  to  the  present  day,  though  we  have  strong 
evidence  to  show  that  if  water  exists  at  all  on  the  moon, 
it  must  be  in  very  small  quantity. 

On  examining  the  moon  with  suitable  magnifying  pow> 
ers,  we  perceive  on  every  part  of  the  surface,  even  in 
the  midst  of  the  so-called  oceans  and  seas,  ring-like  spots, 
evidently  of  volcanic  character,  with  extensive  chains  of 
mountains  and  steep  isolated  rocks,  presenting  altogether 
a  very  rugged  and  desolate  appearance.  If  we  choose 
for  observation  the  first  or  last  quarter  of  the  moon,  the 
portions  near  the  edge  of  the  illuminated  part  appear 
eaten  into  cavities  surrounded  by  circular  walls,  which 
cast  shadows  away  from  the  sun,  at  one  side  towards  the 
interior,  and  on  the  other  towards  the  exterior  of  the 
cavity.  Along  the  whole  line  which  separates  the  light 
and  dark  parts  of  the  moon,  called  the  terminator,  the 
interior  of  the  ring-like  cavities  seems  quite  black,  while 
here  and  there  luminous  points  show  themselves  detached 
from  the  illuminated  portion  of  the  moon. 

These  spots  indicate  mountain  tops  or  ranges,  which, 
according  as  we  observe  them  at  the  first  or  last  quarter, 
are  receiving  the  rays  of  the  moon's  rising  or  setting  sun 
while  the  lowlands  are  in  the  shade. 

Small  spots  of  annular  form,  which  are  regarded  as 
craters,  are  exceedingly  numerous,  and  are  seen  to  cover 
the  whole  visible  surface  of  the  moon.  In  some  places 


136  ASTRONOMY. 

they  are  thickly  crowded  together,  small  volcanoes  hav- 
ing formed  on  the  sides  of  the  large  one  :  in  other  re- 
gions they  are  comparatively  isolated.  Their  dimensions 
are  far  greater  than  those  of  the  largest  volcanoes  on 
the  earth,  the  breadth  of  the  chasm  occasionally  exceed- 
ing one  hundred  miles,  while  the  sides  of  the  mountains 
attain  a  very  considerable  elevation.  The  best  time  for 
viewing  a  crater  is  when  it  is 'just  clear  of  the  dark  part 
of  the  moon,  or  when  the  sun  is  just  above  its  horizon. 
We  can  then  trace  the  shadows  thrown  by  the  side  of 
the  mountain  upon  its  interior  and  exterior  surface,  and, 
by  measuring  these  shadows,  we  may  approximate  to 
the  true  altitude  of  the  mountain.  Some  of  the  steep 
isolated  rocks  throw  their  shadows  for  many  miles  across 
the  plains  surrounding  them. 

Of  course  the  angle  subtended  by  the  shadow  can  be 
directly  measured,  and  since  we  know  the  angle  sub- 
tended by  the  diameter  of  the  moon,  and  the  length  of 
this  diameter  in  miles,  we  can  readily  determine  the 
length  of  the  shadow  in  miles.  It  will  evidently  be  the 
same  fraction  of  the  diameter  in  miles,  as  the  angle  which 
it  subtends  is  of  the  angle  subtended  by  the  diameter  of 
the  moon.  Knowing,  then,  the  length  of  the  shadow  in 
miles,  and  the  height  of  the  sun  above  the  horizon,  we 
can  easily  ascertain  the  height  of  the  mountain  which 
casts  the  shadow. 

We  have  only  to  ascertain  the  length  of  the  shadow 
cast  by  a  mountain  of  known  height  on  the  earth  when 
the  sun  is  the  same  distance  above  the  horizon.  The 
height  of  the  lunar  mountain  will  be  just  as  many  times 
greater  as  its  shadow  is  longer. 

122.  Tycho.  —  One  of  the  most  remarkable  of  the  lu- 
nar spots  is  that  called  Tycho ,  which  is  readily  distin- 
guished in  the  southern  part  of  the  full  moon  by  the 
number  of  luminous  rays,  or  streaks  of  light,  which  di- 


ASTRONOMY. 


-37 


verge  from  it  in  a  northeasterly  direction.  Tycho  is  an 
annular  mountain  or  crater,  no  less  than  fifty-four  miles 
in  diameter.  The  height  of  the  western  wall  above  the 
interior  level  is,  according  to  Madler,  17,100  feet,  and 
of  the  eastern  borders  somewhat  more  than  16,000  feet. 
A  mountain  nearly  a  mile  high  marks  the  centre  of  the 
crater.  Tycho  is  surrounded  by  a  great  number  of  cra- 
ters, peaks,  and  ridges  of  mountains,  lying  so  close  to- 
gether that  in  some  directions  it  is  impossible  to  find 
the  smallest  level  place. 

Figure  63  gives  a  view  of  the  region  to  the  southeast 
of  Tycho, 


Fig.  63. 


This  mountain,  as  we  have  already  said,  is  the  centre 
of  a  number  of  luminous  streaks  or  rays,  which  extend 
therefrom  over  fully  one  fourth  of  the  moon's  disc.  The 
brightest  one  branches  off  in  a  northeasterly  direction, 
and  there  are  others  very  conspicuous  on  the  western 
side  of  the  crater.  These  rays  become  visible  as  soon 


138  ASTRONOMY. 

as  the  sun  has  risen  From  20°  to  25°  above  their  horizon. 
Their  color  is  perhaps  a  little  whiter  or  more  silvery  than 
the  general  lunar  surface.  Many  opinions  have  been 
advanced  by  Cassini,  Schroter,  Herschel,  and  others,  re- 
specting the  nature  of  these  appearances,  and  they  have 
been  variously  styled  mountains,  streams  of  lava,  and 
even  roads.  There  is  nothing  on  the  surface  of  the 
earth  bearing  the  slightest  analogy  to  them.  Perhaps 
the  most  plausible  theory  is  that  first  started  by  Mr.  Nas- 
inyth,  that  they  have  been  caused  by  a  general  volcanic 
upheaval  of  the  moon's  crust  in  former  ages,  which  has 
produced  an  appearance  on  the  lunar  surface  similar  to 
that  of  a  pane  of  glass  broken  by  a  sharp-pointed  in- 
strument. The  mere  fact  of  their  divergence  from  the 
great  crater  Tycho  proves  that  it  was  the  focus  of  this 
volcanic  outbreak,  whenever  it  may  have  occurred. 

123.  Copernicus.  —  Another  very  beautiful  annular  moun- 
tain is  that  known  as  Copernicus,  shown  in  Figure  64. 

The  diameter  of  the  crater  is  somewhat  larger  than 
that  of  Tycho,  being  rather  more  than  fifty-five  miles. 
The  highest  point  is  about  11,250  feet  above  the  sur- 
rounding plains.  It  is  readily  discernible  on  the  full 
moon,  but  is  most  favorably  viewed  when  the  sun's  rays 
have  just  reached  its  eastern  side,  about  the  time  of 
quadrature,  or  first  quarter.  The  shadows  of  the  west- 
ern side  of  the  crater  are  then  thrown  on  the  interior 
level,  that  of  the  central  peak  on  the  same  level  towards 
the  eastern  side,  while  the  shadow  of  this  side  of  the 
mountain  darkens  for  some  distance  the  exterior  plain 
on  the  rugged  edge  of  the  moon.  Generally  speaking, 
these  shadows  are  extremely  well  defined.  The  diver- 
gent streaks  of  light  from  this  mountain  are  best  seen 
near  the  time  of  full  moon.  They  vary  in  breadth  from 
three  to  ten  miles,  the  principal  one  branching  off  to- 
wards the  northeast. 


ASTRONOMY. 

Fig.  64. 


139 


124.  Kepler. — This  is  also  a   conspicuous    ring-moun- 
tain,  the   focus    of  similar  rays  of  light.     The  crater   is 
about  twenty-two  miles  in  diameter,  and  the  altitude  of 
the  eastern  edge  above  the  level  of  the  interior  is  about 
10,000  feet. 

Tycho,  Copernicus,  and  Kepler  are  the  principal  cra- 
ters which  form  the  radiating  points  of  the  luminous 
streaks  which  are  so  remarkable  upon  the  surface  of  the 
full  moon. 

125.  Eratosthenes. — This  is   a   very   beautiful    annular 
mountain    situated    at   the   extremity   of  the    long   range 
called    the    Apennines,    which    cover   a   surface    of   more 
than    16,000  square  miles.     The  crater  is  not  less  than 


14°  ASTRONOMY. 

thirty  ^seven  miles  in  diameter,  and  in  its  centre  a  steep 
rock  rises  15,800  feet  above  the  level  surface  of  the  in- 
terior. The  outside  of  the  circular  mountain  is  about 
3,300  feet  high  on  the  western  border,  while  on  the 
eastern  side  its  height  is  more  than  twice  as  great. 

The  volcanic  character  of  the  lunar  mountains  is  un- 
mistakable. All  the  crust  of  our  satellite  is  pierced  with 
craters  which  indicate  an  innumerable  series  of  volcanic 
eruptions,  some  limited  to  a  small  space,  others  embrac- 
ing an  immense  area. 

The  darkish  portions  of  the  moon  are  supposed  to  be 
large  plains. 

126.  Are  there  Active  Volcanoes  on  the  MOOJI  ?  —  In  1787 
Sir  William  Herschel  announced  that  he  had  observed 
three  volcanoes  in  a  state  of  eruption  in  different  parts 
of  the  moon  ;  and  modern  astronomers  have  repeatedly 
noticed  luminous  spots  in  the  dark  portion  of  the  lunar 
disc,  some  of  which  were  so  distinct  and  striking  that 
they  might  readily  be  taken  for  active  volcanoes.  The 
prevailing  opinion  among  astronomers,  however,  is,  that 
these  appearances  are  due  to  the  reflection  of  the  "  earth- 
light"  (117)  from  certain  mountain  tops,  which  from  their 
nature  or  their  position  have  a  greater  reflective  power 
than  other  parts  of  the  moon. 

Recent  observations,  however,  show  that  changes  of 
some  kind  are  still  going  on  in  lunar  craters.  In  Oc- 
tober and  November,  1866,  Schmidt,  the  Director  of  the 
Observatory  of  Athens,  noticed  that  the  deep  crater  Linrie, 
whose  diameter  is  5.6  miles,  had  completely  disappeared, 
and  in  its  place  there  was  only  "  a  little  whitish  luminous 
cloud."  He  at  once  called  the  attention  of  other  Euro- 
pean astronomers  to  the  facts,  and  in  December  the  lo- 
cality of  the  lost  crater  was  carefully  examined  by  many 
of  them.  All  agreed  with  Schmidt,  that  Linne  could  not 
be  seen  at  the  time  when  it  was  most  favorably  situated 


ASTRONOMY.  141 

for  observation,  and  when  smaller  craters  in  its  immedi- 
ate neighborhood  were  very  distinct  with  the  shadows 
within  them. 

The  obscuration,  whatever  may  have  been  its  cause,  ap- 
pears to  have  ceased  in  the  latter  part  of  December,  when 
the  crater  was  distinctly  seen  by  Dr.  Tietjen  at  Berlin. 

It  is  said  that  one  of  Schroter's  maps  gives  a  dark 
spot  in  the  place  of  Linne',  and  that  the  crater  is  not  to 
be  found  on  Russell's  globe  or  maps  of  the  year  1797; 
from  which  it  may  be  inferred  that  the  crater  has  previ- 
ously been  obscured.* 

127.  The  Moon  has  little  or  no  Atmosphere.  —  If  there 
is  a  lunar  atmosphere,  it  must  be  one  of  great  rarity  and 
of  no  great  extent ;  otherwise  it  would  give  rise  to  phe- 
nomena which  could  not  fail  to  attract  the  attention  of 
astronomers. 

The  two  main  reasons  for  thinking  that  there  is  no 
atmosphere  of  any  considerable  density  at  the  moon  are, 
(i.)  the  sharpness  of  the  line  which  separates  the  bright 
and  dark  portions  of  her  disc,  and  (2.)  the  absence  of 
refraction,  as  shown  in  the  occultation  of  stars. 

(i.)  It  is  well  known  that  there  is  no  gradual  shading 
off  from  the  illuminated  parts  of  the  moon's  disc,  as  there 
appears  to  be  in  the  case  of  Mercury  and  Venus,  and 
as  there  is  known  to  be  in  the  case  of  the  earth.  There 
is,  therefore,  no  perceptible  twilight  on  the  moon,  and 
consequently  no  atmosphere,  unless  of  great  rarity. 

(2.)  According  to  the  well-known  laws  of  refraction, 
if  there  were  an  atmosphere  about  the  moon,  the  rays  of 
light  would  be  so  bent  that  a  star,  on  passing  behind 
the  moon,  would  be  seen  even  after  it  was  really  be- 
hind the  disc,  just  as  the  sun  is  visible  after  it  is  really 
below  the  horizon  ;  and  so  that  it  would  become  visible 
before  it  had  really  emerged  from  behind  the  disc,  just 
*  See  Appendix,  V. 


142  ASTRONOMY. 

as  the  sun  is  visible  before  it  is  really  above  the  horizon. 
It  would  then  follow  that  a  star  would  appear  to  be  be- 
hind the  moon  a  shorter  time  than  that  computed  from 
the  known  rate  of  motion  and  angular  diameter  of  the 
moon.  Now  it  is  found  tliat  the  observed  time  of  the 
occultation  of  any  star  by  the  moon  is  very  slightly,  if 
at  all,  shorter  than  the  computed  time.  Airy  has  shown 
that,  if  the  discrepancy  of  2 "which  he  has  found  (118) 
between  the  angular  diameter  of  the  moon,  as  determined 
by  observation,  and  as  computed  from  the  rate  of  the 
moon's  motion  and  the  time  of  the  occultation  of  a  star, 
is  wholly  due  to  refraction  caused  by  a  lunar  atmosphere, 
the  refractive  power  of  that  atmosphere  is  only  ^oW 
part  of  that  of  the  earth's  atmosphere ;  hence  it  must 
be  of  extreme  tenuity. 

If  there  is  no  atmosphere  at  the  moon,  there  can  be 
no  water  on  her  surface;  for  the  heat  of  the  sun  would 
cause  that  water  to  evaporate,  and  thus  an  atmosphere 
of  aqueous  vapor  would  be  formed. 

, Furthermore,  there  has  never  been  discovered  any  posi- 
tive evidence  of  the  existence  of  clouds  at  the  moon, 
which  would  be  the  necessary  result  of  the  existence  of 
water  there. 

Some  astronomers  have  supposed  that  the  side  of  the 
moon  turned  towards  us  may  be  a  huge  mountain,  and 
that  there  may  really  be  both  air  and  water  on  the  far- 
ther side,  though  not  enough  to  rise  above  this  moun- 
tain. Both  Adams  and  Le  Verrier  have,  however,  shown 
that  such  a  hypothesis  is,  to  say  the  least,  extremely 
improbable. 

ECLIPSES. 

128.  The  Shadows  of  the  Earth  and  Moon.  —  The  earth 
and  moon  are  two  spherical  and  opaque  bodies,  and  the 
halves  of  both  are  constantly  illuminated  by  the  rays  of 


ASTRONOMY.  143 

the  sun,  while  the  other  halves  are  in  the  shade.  The 
illuminating  body  is  itself  a  sphere  of  much  greater  size. 
Not  only,  therefore,  have  the  earth  and  the  moon  always 
one  of  their  hemispheres  dark,  but  each  of  these  bodies 
throws  behind  it,  in  a  direction  opposite  from  the  sun, 
a  shadow  of  conical  form,  the  length  and  diameter  of 
which  depend  upon  the  distance  and  diameter  of  the  il- 
luminating body,  and  the  diameter  of  the  illuminated 
body. 

This  cone  of  shade  encloses  all  those  parts  of  space 
where,  by  reason  of  the  interposition  of  the  opaque  body, 
no  rays  of  light  from  the  sun  can  be  received.  Beyond 
the  apex  of  this  cone  of  pure  shade,  which  is  called  the 
umbra,  and  in  the  direction  of  its  axis,  are  situated  those 
portions  of  space  from  which  a  part  of  the  sun  is  seen 
in  the  form  of  a  luminous  ring  bordering  the  obscure 
disc  of  the  opaque  body.  Lastly,  these  two  regions  are 
themselves  surrounded  by  what  is  called  the  penumbra; 
or  those  portions  of  space  which  receive  light  only  from 
a  part  of  the  sun,  one  side  of  whose  luminous  disc,  is 
obscured  by  the  disc  of  the  opaque  body.  The  dark- 
ness of  the  penumbra  at  any  point  is  more  intense,  in 
proportion  as  the  point  is  nearer  the  umbra. 

The  moon  and  the  earth  in  their  movements  carry 
with  them  their  cones  of  umbra  and  penumbra,  and  it 
is  by  projecting  these  total  or  partial  shadows  upon  each 
other  that  they  produce  the  phenomena  of  eclipses. ' 

These  various  cones  are  represented  in  Figure  65. 

129.  When  Eclipses  may  Occur.  —  On  examining  this 
figure,  it  will  be  seen  at  once  why  an  eclipse  of  the  sun 
can  happen  only  at  the  time  of  new  moop,  and  why,  on 
the  other  hand,  an  eclipse  of  the  moon  is  possible  only 
at  full  moon. 

In  all  other  positions  of  the  moon,  her  cone  of  shade 
is  projected  into  space  away  from  the  earth,  and  the 


144 


ASTRONOMY. 


errestrial  cone  of  shade  does  not  meet  the  moon.  It 
does  not  follow,  however,  that  there  is  an  eclipse  of  the 
sun  at  every  new  moon,  or  of  the  moon  at  every  full 
moon.  This  would  be  true  if  the  orbits  of  the  earth 
round  the  sun  and  of  the  moon  round  the  earth  were 
described  in  the  same  plane.  Then  at  each  opposition 
or  conjunction  the  centres  of  the  three  bodies  would 
necessarily  lie  in  a  straight  line. 

But  the  orbit  of  the  moon  is  inclined  to  the  ecliptic 


ASTRONOMY.  145 

at  an  angle  of  about  5°,  so  that  it  often  happens  at  the 
time  of  new  moon  that  our  satellite  throws  its  cone  of 
shadow  above  or  below  the  earth.  In  like  manner,  at 
the  time  of  opposition,  the  moon,  in  consequence  of  her. 
being  out  of  the  plane  of  the  ecliptic,  passes  sometimes 
above  and  sometimes  below  the  cone  of  the  earth's  shadow. 
In  such  cases  there  can  be  no  eclipse. 

In  order,  then,  that  there  should  be  an  eclipse  of  the 
sun,  new  moon  must  occur  when  the  moon  is  at  or  near 
one  of  the  nodes  (67)  of  her  orbit;  and  in  order  that 
there  should  be  an  eclipse  of  the  moon,  full  moon  must 
occur  when  the  moon  is  at  or  near  one  of  her  nodes. 

130.  Eclipses  of  the  Sun.  —  Solar  eclipses  are  of  three 
kinds.  When  the  dark  disc  of  the  moon  entirely  covers 
the  sun,  the  eclipse  is  total;  when  only  a  portion,  large 
or  small,  of  one  side  of  the  sun  is  covered  by  the  moon, 
the  eclipse  is  partial ' ;  and  when  the  disc  of  the  moon 
is  not  large  enough  to  cover  the  whole  disc  of  the  sun, 
and  thus  leaves  a  luminous  ring  visible  around  its  own 
body,  the  eclipse  is  annular. 

As  the  moon  is  much  smaller  than  the  sun,  it  will  be 
understood  that  it  is  her  small  relative  distance  that 
causes  her  disc  to  appear  equal  to  or  greater  than  that 
of  the  sun.  This  distance  varies  by  reason  of  the  ellip- 
tical form  of  the  moon's  orbit,  and  hence  the  lunar  disc 
is  sometimes  larger,  sometimes  smaller  than,  and  some- 
times equal  to,  that  of  the  sun. 

This  is  the  same  as  saying  that  the  cone  of  the  moon's 
real  shadow,  or  umbra,  sometimes  reaches  the  earth  and 
sometimes  does  not.  If  it  reaches  the  earth  there  is  a 
total  eclipse  of  the  sun  to  all  parts  of  the  earth  within 
it,  and  a  partial  eclipse  to  all  parts  within  the  penumbra. 
This  will  be  readily  seen  from  Figure  66. 

If  the  cone  of  the  lunar  shadow  does  not  reach  the 
earth,  there  will  be  an  annular  eclipse  in  those  places 
7  J 


which  are  in  the  direction  of  the  axis  of  the  cone,  and 
a  partial  eclipse  to  those  which  are  only  within  the  pe- 
numbra. This  case  is  represented  in  Figure  67. 

Fig.  67. 


It  will  be  seen,  then,  that  the  conditions  under  which 
a  total  eclipse  of  the  sun  is  possible  are  the  following:  — 
(i.)  the  moon  must  be  in  conjunction,  or  new ;  (2.)  she 
must  at  the  same  time  be  at  or  near  a  node ;  (3.)  her 
distance  from  the  earth  must  be  less  than  the  length 
of  her  shadow. 

The  same  conditions,  except  the  last,  are  necessary  for 
an  annular  eclipse. 

The  breadth  of  the  cone  of  the  moon's  umbra  at  the 
distance  of  the  earth  seldom  equals  160  miles.  Hence 
a  total  eclipse  is  seen  only  over  a  very  narrow  tract ; 
but,  owing  to  the  rotation  of  the  earth,  this  tract  has  con- 
siderable length. 


ASTRONOMY.  147 

A  total  eclipse  of  the  sun  is  a  rare  occurrence  at  best, 
and  a  total  eclipse  at  any  given  place  is  rarer  still.  It 
will  be  seen  from  Figure  67  that  even  the  penumbra  of 
the  moon's  shadow  traverses  but  a  small  part  of  the 
earth ;  so  that  a  partial  eclipse  of  the  sun  is  by  no  means 
visible  to  the  whole  earth. 

Hind  thus  describes  the  appearances  during  the  total 
eclipse  of  the  sun,  July  28th,  1851,  in  Sweden:  — 

"The  aspect  of  nature  during  a  total  eclipse  was  grand 
beyond  description.  A  diminution  of  light  over  the  earth 
was  perceptible  a  quarter  of  an  hour  after  the  beginning 
of  the  eclipse,  and  about  ten  minutes  before  the  extinc- 
tion of  the  sun  the  gloom  increased  very  perceptibly. 
The  distant  hills  looked  dull  and  misty,  and  the  sea  as- 
sumed a  dusky  appearance,  like  that  it  presents  during 
rain.  The  daylight  that  remained  had  a  yellowish  tinge, 
and  the  azure  blue  of  the  sky  deepened  to  a  purplish- 
violet  hue,  particularly  towards  the  north.  But,  notwith- 
standing these  gradual  changes,  the  observer  could  hardly 
be  prepared  for  the  wonderful  spectacle  that  presented 
itself  when  he  withdrew  his  eye  from  the  telescope,  after 
the  totality  had  come  on,  to  gaze  around  him  for  a  few 
seconds.  The  southern  heavens  were  then  of  a  uniform 
purple-gray  color,  the  only  indication  of  the  sun's  posi- 
tion being  the  luminous  corona,  the  light  of  which  con- 
trasted strikingly  with  that  of  the  surrounding  sky.  In 
the  zenith,  and  north  of  it,  the  heavens  were  of  a  pur- 
plish-violet, and  appeared  very  near,  while  in  the  north- 
west and  northeast,  broad  bands  of  yellowish-crimson  light, 
intensely  bright,  produced  an  effect  which  no  person  who 
witnessed  it  can  ever  forget.  The  crimson  appeared  to 
run  over  large  portions  of  the  sky  in  these  directions  ir- 
respective of  the  clouds.  At  higher  altitudes  the  pre- 
dominant color  was  purple.  All  nature  seemed  to  be 
overshadowed  by  an  unnatural  gloom,  the  distant  hills 


148  ASTRONOMY. 

were  hardly  visible ;  the  sea  turned  lurid  red,  and  per- 
sons standing  near  the  observer  had  a  pale,  livid  look, 
calculated  to  produce  the  most  painful  sensations.  The 
darkness,  if  it  can  be  so  termed,  had  no  resemblance  to 
that  of  night.  At  various  places  within  the  shadow,  the 
planets  Venus,  Mercury,  and  Mars,  and  the  brighter  stars 
of  the  first  magnitude,  were  plainly  seen  during  the  to- 
tal eclipse.  Venus  was  distinctly  visible  at  Copenhagen, 
though  the  eclipse  was  only  partial  in  that  city;  and  at 
Dantzic  she  continued  in  view  ten  minutes  after  the  sun 
had  reappeared.  Animals  were  frequently  much  affected. 
At  Engelholm,  a  calf  which  commenced  lowing  violently 
as  the  gloom  deepened,  and  lay  down  before  the  totality 
had  commenced,  went  on  feeding  quietly  enough  very 
soon  after  the  return  of  daylight.  Cocks  crowed  at  Hel- 
singborg,  though  the  sun  was  there  hidden  only  thirty 
seconds,  and  the  birds  sought  their  resting-places  as  if 
night  had  come  on." 

131.  Eclipses  of  the  Moon.  — Like  the  eclipses  of  the 
sun,  those  of  the  moon  may  be  either  total  or  partial,  but 
they  are  never  annular,  since  the  breadth  of  the  cone 
of  the  earth's  shadow  at  the  distance  of  the  moon  is  al- 
ways much  greater  than  the  diameter  of  the  moon's  disc. 

The  fundamental  difference  between  the  two  phenom- 
ena is,  that  an  eclipse  of  the  sun  is  visible  to  only  a  part 
of  the  hemisphere  which  has  him  above  the  horizon, 
while  an  eclipse  of  the  moon  is  visible  from  every  part 
of  the  earth  from  which  the  moon  herself  is  visible ;  and 
an  eclipse  of  the  sun  is  seen  at  different  stations  succes- 
sively, as  the  umbra  and  penumbra  of  the  moon's  shadow 
traverse  the  earth,  while  an  eclipse  of  the  moon  every- 
where begins  and  ends  at  the  same  instant.  The  reason 
of  this  difference  is  that  the  sun's  disc  is  not  really  dark- 
ened, but  only  hidden  by  the  obscure  disc  of  the  moon, 
so  that  the  interposition  is  an  effect  of  perspective,  vary- 


ASTRONOMY.  149 

ing  according  to  the  respective  position  of  the  observer, 
of  the  moon,  and  of  the  sun.  The  lunar  eclipse  is,  on  the 
contrary,  produced  by  the  real  fading  out  of  the  moon's 
light,  and  the  darkness  consequent  upon  it  is  observed  at 
the  same  instant  wherever  the  moon  is  in  view. 

When  the  moon  passes  through  the  centre  of  the  earth's 
shadow  the  eclipse  is  total  and  central.  The  earth's  shad- 
ow at  the  moon's  distance  is,  however,  so  broad  that  an 
eclipse  may  be  total  without  being  also  central. 

The  magnitude  of  an  eclipse,  if  partial,  and  the  contin- 
uance of  the  obscuration,  if  total,  depend  upon  the  direc- 
tion of  the  moon's  passage  through  the  earth's  shadow, 
which  is  sufficiently  broad  to  allow  of  her  being  hidden 
by  it  one  hour  and  fifty  minutes,  when  she  passes  through 
its  centre. 

It  is  not  possible  to  ascertain,  with  any  degree  of  accu- 
racy, the  time  when  the  moon  first  enters  the  penumbra, 
for  the  darkening  effect  upon  her  disc  is  so  slight  that 
some  minutes  must  elapse  before  sufficient  shade  is  pro- 
duced to  attract  attention.  Neither  does  the  time  of 
contact  with  the  umbra  admit  of  exact  observation,  since 
the  penumbra  shades  off  into  the  umbra  by  imperceptible 
degrees. 

When  the  moon  is  totally  immersed  in  the  dark  shad- 
ow, she  does  not,  except  on  rare  occasions,  become  in- 
visible, but  assumes  a  dull  reddish  hue,  somewhat  like 
that  of  tarnished  copper.  This  arises  from  the  refraction 
of  the  sun's  rays  in  passing  through  the  earth's  atmos- 
phere. 

In  a  total  lunar  eclipse  in  1848,  the  spots  on  the  moon's 
surface  were  distinctly  seen  by  many  observers,  and  the 
general  color  of  the  moon  was  a  full  glowing  red.  Her 
appearance  was  so  singular  that  many  persons  doubted 
of  her  being  eclipsed  at  all. 

Once  in  about  eighteen  years  the  earth,  sun,  and  moon 


150  ASTRONOMY. 

occupy  the  same  relative  positions.  This  is  a  fact  which 
the  ancients  established  by  observation  long  before  the 
theory  of  the  celestial  movement's  had  demonstrated  its 
near  approach  to  the  truth.  If,  then,  we  start  from  the 
epoch  of  an  eclipse  of  the  sun  or  moon,  that  is  to  say, 
from  a  lunar  conjunction  or  opposition  coinciding  with 
one  of  the  moon's  nodes,  after  18  years  the  three  bodies 
will  be  found  in  situations  nearly  identical.  Hence  the 
eclipses  which  succeeded  one  another  in  the  first  pe- 
riod follow  again  in  the  same  order  during  the  second 
period.  This  is  the  starting  point  in  the  calculation  of 
eclipses,  but  the  approximation  is  too  rough  for  the  ex- 
actness of  modern  astronomy.  Now-a-days  the  time  of 
eclipses  is  foretold  to  a  second  several  years  in  advance 
of  their  occurrence. 

132.  O captations.  —  The  moon  in  traversing  her  orbit 
round  the  earth  produces  another  kind  of  eclipse,  to 
which  the  name  of  occultation  has  been  given.  A  star 
or  planet  is  said  to  be  occulted  when  it  passes  behind 
the  lunar  disc.  These  phenomena  have  already  been 
mentioned  with  reference  to  the  question  of  the  existence 
of  an  atmosphere  on  the  surface  of  the  moon  (127). 

The  occultations  of  the  stars  are  calculated  with  the 
same  precision  as  the  eclipses,  and  as  they  are  of  fre- 
quejit  occurrence  they  are  of  great  use  to  navigators  in 
determining  their  longitude.  As  the  moon  is  very  near 
the  earth,  compared  with  the  distance  of  the  stars  and 
even  of  the  planets,  it  follows  that  two  observers  at  dif- 
ferent points  on  the  earth  do  not  see  it  projected  at  the 
same  instant  on  the  same  part  of  the  heavens.  The  oc- 
cultation of  a  star  does  not,  therefore,  take  place  to  both 
of  them  at  the  same  instant  of  time. 

By  correcting  these  observations  for  refraction  and  par- 
allax, the  exact  time  is  found  at  which  an  occultation 
would  take  place  to  an  observer  at  tne  centre  of  the 


ASTRONOMY.  151 

earth.  Now  the  times  at  which  the  occupation  of  stars 
would  occur  to  an  observer  situated  at  the  centre  of 
the  earth  are  computed  in  Greenwich  time  and  published 
in  the  Nautical  Almanac.  An  observer  at  sea,  then,  finds 
by  observation  the  time  of  occultation  as  seen  from  the 
earth's  centre  in  his  own  local  time,  and  he  can  then 
compare  his  own  local  time  with  Greenwich  time,  and 
find  the  difference  between  the  two.  He  can  then  readi- 
ly determine  the  longitude  of  his  place. 

As  we  have  already  seen,  the  meridian  of  a  place  sweeps 
over  the  whole  heavens,  from  the  sun  around  to  it  again, 
in  twenty-four  hours.  Hence  it  will  sweep  over  15°  in 
one  hour,  and  i°  in  four  minutes;  and  when  the  sun  is 
on  the  meridian  of  a  given  place,  it  will  be  15°  east  of 
the  meridian  of  a  place  15°  to  the  west  of  it.  The  sun 
will  then  come  upon  the  meridian  an  hour  later  at  the 
second  place,  and  it  will  be  one  o'clock  at  the  more  east- 
erly place  when  it  is  twelve  o'clock  at  the  more  westerly. 
Hence  local  time  becomes  an  hour  earlier  as  we  travel 
westward  15°. 

If,  then,  we  know  that  Greenwich  time  is  three  hours 
later  than  our  time,  we  know  that  we  are  45°  west  from 
Greenwich ;  and  if  Greenwich  time  is  two  hours  earlier 
than  our  time,  we  know  that  we  are  30°  east  of  that  place, 
or  that  we  are  in  longitude  30°  east. 

Not  only  is  the  time  at  which  the  occultation  of  the 
star  would  occur  to  an  observer  at  the  centre  of  the 
earth  computed  in  Greenwich  time  and  published  in  the 
Nautical  Almanac,  but  also  the  time  when  the  moon 
passes  all  the  principal  stars  near  her  path  is  computed 
and  published  in  the  same  manner,  as  well  as  the  distance 
of  the  moon  from  these  principal  stars  for  every  day  dur- 
ing the  year. 

Thus  the  heavens  become  a  universal  dial  over  which 
the  moon  sweeps  as  a  minute-hand,  marking,  as  she  passes 


152  ASTRONOMY. 

the  fixed  stars,  Greenwich  time  to  every  part  of  the 
earth. 

But  this  hand  moves  with  considerable  unsteadiness, 
now  faster  and  now  slower,  according  as  the  moon  is  at 
perigee  or  apogee,  and  subject  to  various  other  fluctu- 
ations ;  while  by  reason  of  parallax  and  refraction  her 
real  position  in  front  of  the  dial  is  seldom  what  it  ap- 
pears to  be,  so  that  it  has  required  the  patient  observa- 
tion and  study  of  years  to  learn  to  read  this  time  aright. 

The  learning  to  read  time  accurately  by  this  clock  of 
nature  has  been  one  of  the  greatest  triumphs  of  astron- 
omy, and  is  a  good  illustration  of  the  practical  bearing 
of  such  scientific  studies. 

SUMMARY   OF   THE  MOON   AND   ECLIPSES. 

The  mean  distance  of  the  moon  is  about  thirty  diameters 
of  the  earth;  her  mean  angular  diameter  about  31';  the 
inclination  of  her  orbit  to  the  ecliptic  about  5°;  her  si- 
dereal period  about  27 J  days;  and  her  sy nodical  period 
about  29^  days.  (114.) 

The  phases  of  the  moon  depend  upon  the  position  of 
her  visible  with  reference  to  her  enlightened  hemisphere. 
They  repeat  themselves  after  the  interval  of  a  synodical 
revolution.  (115.) 

The  moon  completes  a  rotation  on  her  axis  in  the 
same  time  that  she  completes  a  revolution  about  the 
earth.  Her  rotation  on  her  axis  is  performed  at  a  uni- 
form rate,  while  the  rate  of  her  revolution  about  the 
earth  varies.  This  gives  rise  to  libration  in  longitude.  The 
axis  of  the  moon  is  not  quite  perpendicular  to  the  plane 
of  her  orbit.  This  gives  rise  to  libration  in  latitude.  We 
see  the  moon  from  a  point  about  4,000  miles  above  the 
centre  of  the  earth.  This  gives  rise  to  parallactic  libra- 
tion. (116.) 


ASTRONOMY.  153 

The  earth  presents  to  the  moon  phases  similar  to  those 
which  the  moon  presents  to  us.  When  it  is  new  moon  to 
us,  it  is  full  earth  to  the  moon.  (117.) 

The  moon  is  nearest  to  us  when  she  is  in  the  zenith, 
but  she  appears  largest  when  she  is  near  the  horizon. 
Owing  to  her  brightness,  the  moon  appears  larger  than 
she  really  is.  (118.) 

The  moon  describes  an  epicycloidal  path,  every  part  of 
which  is  concave  toward  the  sun.  (119.) 

The  least  difference  between  two  successive  risings  of 
the  moon  in  our  latitude  is  about  twenty-three  minutes. 
When  this  least  difference  occurs  at  the  time  of  full 
moon,  we  have  what  is  called  the  Harvest  Moon.  (120.) 

The  surface  of  the  moon  is  covered  with  steep  iso- 
lated rocks,  volcanic  craters,  and  extensive  mountain 
chains.  The  existence  of  these  rocks  and  mountains  is 
indicated  by  the  shadows  which  they  cast.  By  means 
of  these  shadows  we  can  estimate  the  height  of  the  ob- 
jects which  cast  them.  (121.) 

The  four  most  remarkable  lunar  mountains  are  Tycho, 
Copernicus,  Kepler,  and  Eratosthenes.  (122-125.) 

There  is  no  evidence  of  active  volcanoes  on  the  moon, 
though  changes  of  some  kind  are  still  going  on  within  the 
lunar  craters.  (126.) 

That  the  moon  has  little  or  no  atmosphere  is  shown 
by  the  sharpness  of  the  line  which  separates  the  bright 
and  dark  portions  of  her  disc,  and  by  the  absence  of  re- 
fraction. (127.) 

The  earth  and  the  moon  cast  conical  shadows  behind 
them.  (128.) 

When  the  earth  passes  through  the  shadow  of  the 
moon,  there  is  an  eclipse  of  the  sun,  which  may  be  partial, 
annular,  or  total.  This  can  happen  only  at  the  time  of 
new  moon,  and  when  the  moon  is  near  her  node.  As 
the  moon's  shadow  barely  reaches  the  earth,  total 
7* 


154  ASTRONOMY. 

eclipses  of  the  sun  are  of  rare  occurrence  and  of  short 
duration.     (129,  130.) 

When  the  moon  passes  through  the  shadow  of  the 
earth,  there  is  an  eclipse  of  the  moon,  which  may  be  either 
partial  or  total.  This  can  happen  only  at  full  moon,  and 
when  the  moon  is  near  one  of  her  nodes.  In  an  eclipse 
of  the  moon  her  light  is  extinguished,  while  in  an  eclipse 
of  the  sun  his  light  is  only  hidden  by  the  moon.  (129, 

131.) 

The  planets  and  stars  are  occulted  by  the  moon,  and 
by  their  occultation  longitude  at  sea  is  determined.  The 
heavens  are  a  universal  dial,  upon  which  the  moon  points 
Greenwich  time  to  every  part  of  the  earth.  (132.) 

METEORIC  RINGS. 

133.  Shooting  stars  are  those  evanescent  meteors  which 
dart  across  the  sky  at  night  in  all  directions,  and  gener- 
ally leave  behind  them  luminous  trains  visible  some  sec- 
onds after  the  extinction  of  the  brighter  part.  The  num- 
ber of  the  shooting  stars  varies  greatly  with  the  time  of  the 
year  ;  hence  the  distinction  between  sporadic  meteors  and 
the  showers  of  shooting  stars  which  appear  in  the  sky  in 
large  numbers  and  generally  periodically.  During  ordi- 
nary nights,  the  mean  number  of  shooting  stars  observed 
in  the  interval  of  an  hour  is  from  four  to  five,  according 
to  some  observers,  and  as  high  as  eight,  according  to 
others. 

But  at  two  periods  of  the  year,  about  the  loth  of  Au- 
gust and  the  i2th  of  November,  these  phenomena  are 
much  more  numerous,  and  the  number  of  shooting  stars 
observed  in  the  interval  of  an  hour  is  often  more  than 
tenfold  that  seen  on  ordinary  nights.  The  August  show- 
ers used  to  be  popularly  known  as  "  St.  Lawrence's  tears  "  ; 
the  luminous  trains  being  nothing  else  to  the  untutored 


ASTRONOMY.  1 55 

people  of  Ireland  than  the  burning  tears  of  that  martyr, 
whose  feast  fell  on  the  zoth  of  August.  The  November 
shower  is  usually  more  brilliant  than  the  August,  and 
at  intervals  of  about  thirty-three  years  it  is  of  extraordi- 
nary splendor. 

On  the  1 2th  of  November,  1799,  Humboldt,  who  was 
then  at  Cumana,  relates  that,  between  the  hours  of  two 
and  five  in  the  morning,  the  sky  was  covered  with  innu- 
merable luminous  trains,  which  incessantly  traversed  the 
celestial  vault  from  north  to  south,  presenting  the  ap- 
pearance of  fire-works  let  off  at  an  enormous  height ; 
large  meteors,  having  sometimes  an  apparent  diameter  of 
one  and  a  half  times  that  of  the  moon,  blending  their 
trains  with  the  long,  luminous,  and  phosphorescent  paths 
of  the  shooting  stars.  In  Brazil,  Labrador,  Greenland, 
Germany,  and  French  Guiana,  the  same  phenomena  were 
observed. 

The  shower  of  November  i2th,  1833,  was  no  less  ex- 
traordinary. The  meteors  were  observed  along  the  east- 
ern coast  of  America,  from  the  Gulf  of  Mexico  as  far  as 
Halifax,  from  nine  o'clock  in  the  evening  till  sunrise,  and 
in  some  places,  even  in  full  daylight,  at  eight  o'clock 
in  the  morning.  They  were  so  numerous,  and  visible  in 
so  many  parts  of  the  sky  at  once,  that  in  trying  to  count 
them  one  could  only  hope  to  arrive  at  a  very  rough  ap- 
proximation. At  Boston,  Prof.  Olmsted  compared  the 
shower,  at  the  moment  of  maximum,  to  half  the  num- 
ber of  flakes  which  one  sees  in  the  air  during  an  ordinary 
snow-storm.  When  the  brilliancy  of  the  display  was 
considerably  reduced  he  counted  six  hundred  and  fifty  in 
fifteen  minutes,'  though  he  confined  his  observations  to  a 
zone  which  was  not  a  tithe  of  the  visible  horizon.  He 
estimated  that  the  number  he  counted  was  not  more 
than  two  thirds  of  the  number  which  fell ;  making  the 
whole  number  866  in  the  zone  observed,  and  some  8,660 
in  all  the  visible  heavens. 


156  ASTRONOMY. 

Now  the  phenomena  lasted  more  than  seven  hours, 
and  as  the  above  estimate  would  give  an  average  of 
34,640  an  hour,  the  number  seen  at  Boston  exceeded 
240,000  ;  and  yet  it  must  be  remembered  that  the  basis 
of  this  calculation  was  obtained  at  a  moment  when  the 
display  was  notably  on  the  decline. 

Again,  on  the  morning  of  the  i4th  of  November,  1866, 
an  extraordinary  display  of  meteors  was  seen  in  England. 
The  display  was  very  brilliant,  but  those  who  saw  both, 
pronounced  it  much  less  splendid  than  the  show  of  1833. 

134.  The  Probable  Cause  of  these  Phenomena.  —  The 
great  majority  of  the  meteors  of  the  November  shower 
radiate  in  all  directions  from  a  point  in  Leo,  called 
from  this  fact  the  radiant  point ;  while  the  radiant  point 
of  the  August  shower  is  in  Perseus.  These  points  are 
precisely  those  toward  which  the  earth  is  moving  at  the 
time. 

Astronomers  have  therefore  concluded  that  the  appear- 
ance of  shooting  stars  is  caused  by  the  passage  of  the 
earth  through  rings  composed  of  myriads  of  these  bodies, 
which  circulate,  like  the  larger  planets,  round  the  sun,  and 
whose  parallel  movements,  seen  from  the  earth,  seem  to 
radiate  from  that  part  of  the  heavens  which  the  earth  is 
approaching.  The  appearance  required  by  this  theory  is 
exactly  that  presented  to  us. 

Professor  Newton,  of  New  Haven,  an  astronomer  who 
has  given  much  attention  to  this  subject,  finds  that  the 
average  number  of  meteors  which  traverse  the  atmosphere 
daily,  and  which  are  large  enough  to  be  visible  to  the 
naked  eye  on  a  dark,  clear  night,  is  no  less  than  7,500,000  ; 
and  applying  the  same  reasoning  to  telescopic  meteors,  the 
number  will  have  to  be  increased  to  400,000,000. 

It  is  now  generally  held,  that  these  little  bodies  are  not 
scattered  uniformly  throughout  space,  or  collected  into 
either  one  or  two  rings,  but  that  they  are  collected  into 


ASTRONOMY.  157 

several  rings  round  the  sun  ;  and  that,  when  the  earth  in 
its  orbit  breaks  through  one  of  these  rings,  or  passes  near 
it,  her  attraction  overpowers  that  of  the  sun,  and  causes 
them  to  impinge  on  our  atmosphere,  where,  their  motion 
being  arrested  and  converted  into  heat  and  light,  they 
become  visible  to  us  as  meteors,  fire-balls,  or  shooting 
stars,  according  to  their  size. 

It  has  been  suggested,  not  without  some  probability, 
that  the  earth's  attraction  may  sometimes  retain  these 
meteors  as  permanent  satellites.  A  French  astronomer 
believes  he  has  detected  one  of  these  bodies  that  revolves 
around  our  globe  in  a  period  of  three  hours  and  twenty 
minutes.  The  distance  of  this  singular  companion  of 
the  moon  is  5,000  miles  from  the  surface  of  the  earth. 
Occasionally  these  meteors  are  drawn  to  the  earth  by  its 
superior  attraction,  and  fall  to  the  ground  as  meteoric 
stones. 

MARS. 

135.  His  Distance,  Period of 'Revolution ,  etc.  —  The  next 
planet  in  the  order  of  distance  from  the  sun  is  Mars. 
He  is  consequently  the  first  of  those  planets  whose  orbit 
encloses  that  of  the  earth,  and  which  have  therefore  been 
called  exterior  or  superior  planets.  '  Mars  appears  to  the 
naked  eye  as  the  reddest  star  in  the  heavens. 

His  mean  distance  from  the  sun  is  145,000,000  miles, 
but,  in  consequence  of  the  eccentricity  or  ^flattened  form 
of  his  orbit,  he  is  about  27,000,000  miles  nearer  the  sun 
at  perihelion  than  at  aphelion.  His  sidereal  period  is 
somewhat  less  than  two  years,  and  his  synodical  period 
somewhat  more  than  two  years. 

The  plane  of  Mars's  orbit  is  inclined  to  the  ecliptic 
at  an  angle  of  less  than  2°.  The  apparent  diameter  of 
the  planet  varies  considerably,  since  his  distance  from 
the  earth  varies  considerably.  He  must  be  the  diameter 


158  ASTRONOMY. 

of  the  earth's  orbit  nearer  to  us  at  opposition  than  at 
conjunction.  When  nearest  the  earth  his  diameter  sub- 
tends an  angle  of  more  than  30",  while  at  his  greatest 
distance  the  diameter  subtends  an  angle  of  only  4".  The 
real  diameter  of  this  planet  is  about  4,500  miles.  When 
examined  with  a  telescope  of  sufficient  power,  the  disc 
of  Mars  appears  perfectly  round  at  opposition  and  con- 
junction, while  in  every  other  part  of  his  orbit  the  disc 
is  more  or  less  gibbous,  according  to  the  distance  of  the 
planet  from  quadrature,  when  the  illuminated  disc  differs 
most  from  a  circle.  These  phases  prove  that  Mars,  like 
Mercury  and  Venus,  shines  with  light  borrowed  from  the 
sun.  At  opposition  and  conjunction  he  turns  the  same 
face  toward  us  and  toward  the  sun,  and  hence  we  see 
the  whole  of  his  illuminated  hemisphere ;  while  in  other 
parts  of  his  orbit  he  does  not  turn  quite  the  same  face  to 
us  and  to  the  sun,  hence  he  appears  more  or  less  gibbous. 
This  planet  is  most  favorably  situated  for  observation 
at  perihelion  and  opposition.  Opposition  occurs,  as  al- 
ready stated,  once  in  a  little  over  two  years ;  and  opposi- 
tion and  perihelion  occur  together  once  in  about  eight 
years. 

136.  The  Physical  Characteristics  of  Mars. — When 
viewed  under  proper  Optical  powers,  the  surface  of  this 
planet  presents  outlines  of  seas  and  continents  similar  to 
those  on  our  globe,  and  usually  white  spots  are  discerni- 
ble near  the  poles,  which,  from  their  alternate  diminution 
and  increase,  according  as  one  pole  is  turned  to  or  from 
the  sun,  are  conjectured  to  be  masses  of  snow.  The 
color  of  the  continents  is  a  dull  red  ;  that  of  the  seas 
greenish,  as  by  contrast  with  the  land  it  should  be.  It  is 
this  prevailing  color  of  the  land  which  gives  the  planet 
that  ruddy  light  by  which  it  is  at  all  times  readily  dis- 
tinguished from  the  other  planets  and  from  the  fixed  stars. 
By  observing  the  spots  on  the  surface  the  time  of  the 


ASTRONOMY. 


159 


axial  rotation  of  Mars  has  been  determined  to  be  about 
24^  hours.  His  axis  is  inclined  to  the  plane  of  his  orbit 
at  an  angle  of  about  61°. 

Consequently  Mars  experiences  about  the  same  changes 
of  seasons  as  the  earth,  though  each  season  is  about  twice 
as  long. 

Mars,  like  the  earth,  is  not  perfectly  spherical ;  it  is 
somewhat  flattened  at  the  poles,  though  the  amount  of 
the  flattening  is  not  yet  accurately  ascertained. 

It  is  quite  certain  that  Mars  has  an  atmosphere  of  con- 
siderable density,  since  small  stars  are  obscured  as  they 


l6o  ASTRONOMY. 

approach  its  disc.  The  existence  of  snow  near  the  poles 
proves  that  there  must  be  aqueous  vapor  in  the  atmos- 
phere of  Mars ;  and  the  existence  of  the  aqueous  vapor 
goes  to  prove  that  there  are  seas  on  the  surface  of  the 
planet,  as  is  also  indicated  by  the  greenish  spots. 

Figure  68  shows  the  white  spots,  supposed  to  be  masses 
of  snow,  and  also  the  markings  on  the  disc.  It  will  be 
seen  that  the  spots  are  not  exactly  at  the  poles. 

137.  The  Inner  Group  of  Planets.  —  We  now  see  that 
the  four  planets,  Mercury,  Venus,  the  Earth,  and  Mars, 
form  a  group  of  planets  with  certain  resemblances.  They 
all,  so  far  as  known,  have  an  axial  rotation  of  about 
twenty-four  hours  ;  all  have  atmospheres  ;  they  differ  com- 
paratively little  in  size,  and  are  all  small  in  comparison 
with  another  group  with  which  we  shall  soon  become  ac- 
quainted ;  and  only  one  of  them,  the  earth,  has  a  satellite. 

SUMMARY*  OF  THE  INNER   GROUP  OF 
PLANETS. 

The  first  planet  of  this  group  is  Mercury.  He  revolves 
about  the  sun  in  about  three  months,  and  rotates  on  his 
axis  in  about  twenty-four  hours.  (102.) 

The  orbit  of  Mercury  lies  wholly  within  that  of  the 
earth.  His  diameter  is  somewhat  less  than  one  half  that 
of  the  earth.  He  presents  phases  like  the  moon.  (103.) 

These  phases  are  owing  to  the  fact  that  Mercury  shines 
by  reflected  light.  (104.) 

Schroter  thought  he  detected  spots  on  the  disc  of  Mer- 
cury which  indicate  the  presence  of  mountains.  By  ob- 
serving these  he  decided  that  this  planet  rotates  on  its 
axis  in  about  twenty-four  hours.  (105.) 

The  existence  of  twilight  shows  that  Mercury  has  an 
atmosphere.  (106.) 

The  second  planet  of  this  group  is  Venus.     Her  diam- 


ASTRONOMY.  l6l 

eter  is  a  little  less  than  that  of  the  earth.  She  completes 
a  revolution  round  the  sun  in  about  yj  months,  and  pre- 
sents phases  like  Mercury.  (107.) 

Schroter  detected  slight  irregularities  in  the  terminator 
of  Venus,  which  indicate  the  existence  of  mountains.  By 
observing  certain  spots  he  concluded  that  Venus  rotates 
on  her  axis  in  about  twenty-four  hours.  Venus  also  has 
an  atmosphere.  (108.) 

She  is  believed  to  have  no  satellite.  (109.) 

The  next  and  largest  planet  of  this  group  is  the  earth. 
This  planet  is  attended  by  one  satellite.  (113.) 

The  last  planet  of  the  inner  group  is  Mars.  His  orbit 
lies  wholly  without  that  of  the  earth.  He  revolves  about 
the  sun  in  a  period  of  somewhat  less  than  two  years.  The 
diameter  of  Mars  is  a  little  more  than  half  that  of  the 
earth.  Mars  often  appears  somewhat  gibbous.  (135.) 

His  disc  presents  outlines  of  seas  and  continents  similar 
to  those  which  exist  on  the  earth,  and  white  spots  near 
the  poles,  which  are  thought  to  be  patches  of  snow.  Mars 
resembles  the  earth  in  his  change  of  seasons.  He  also 
has  an  atmosphere  of  considerable  density.  (136.) 

The  four  planets,  Mercury,  Venus,  the  Earth,  and  Mars, 
have  well-marked  resemblances.  They  constitute  what 
may  be  called  the  Inner  Group  of  Planets.  (137.) 

The  Zodiacal  Light  (in,  112)  and  Meteoric  Rings  (133, 
134)  lie  within  the  limits  of  this  group. 

THE   MINOR   PLANETS. 

138.  Bodfs  Law.  —  Between  the  orbit  of  Mars  and 
that  of  Jupiter,  the  next  of  the  planets  known  to  the 
ancients,  there  is  an  interval  of  350,000,000  miles,  in 
which  no  planet  was  known  to  exist  before  the  beginning 
of  the  present  century. 

Three    hundred  years   ago,    Kepler   had    pointed    out 


162  ASTRONOMY. 

something  like  a  regular  progression  in  the  distances  of 
the  planets  as  far  as  Mars,  which  was  broken  in  the 
case  of  Jupiter,  and  he  is  said'  to  have  suspected  the 
existence  of  another  planet  in  the  great  space  separating 
these  two  bodies.  •  The  question  attracted  little  further 
attention  until  Uranus  was  discovered  by  Sir  William 
Herschel  in  1781,  when  several  German  astronomers  re- 
vived the  opinion  held  by  Kepler,  and,  guided  by  a  law 
of  planetary  distances  published  by  Professor  Bode  of 
Berlin,  even  approximated  to  the  period  of  the  supposed 
latent  body.  According  to  this  law,  the  distance  of  a 
planet  is  about  double  that  of  the  next  interior  one,  and 
half  that  of  the  next  exterior  one,  and,  roughly  speak- 
ing, this  rate  of  progression  of  the  planetary  distances 
is  found  to  hold  good  with  this  exception.  Mars  is  sit- 
uated at  a  distance  about  twice  that  of  the  earth,  but 
very  much  less  than  half  that  of  Jupiter ;  and  again,  Ju- 
piter revolves  at  half  the  distance  of  the  next  exterior 
planet,  Saturn,  but  considerably  more  than  twice  that  of 
Mars.  If,  therefore,  another  planet  existed  between 
Mars  and  Jupiter,  the  progression  of  Bode's  law,  instead 
of  being  interrupted  at  this  point,  might  perhaps  be 
found  to  hold  good  as  far  as  Uranus.  For  this  reason, 
an  association  of  astronomers  was  formed,  and  a  regular 
plan  of  search  was  devised  with  a  view  to  the  discovery 
of  the  suspected  planet. 

139.  The  Discovery  of  Ceres.  —  Professor  Piazzi,  Direc- 
tor of  the  Observatory  at  Palermo,  repeatedly  sought  for 
a  star  numbered  in  Wollaston's  Catalogue,  but  finding 
none  in  the  position  there  assigned,  he  observed  all  the 
stars  of  similar  brightness  in  the  vicinity.  On  the  ist 
of  January,  1801,  or  about  the  time  the  search  for  the 
supposed  body  was  begun,  he  determined  the  place  of 
an  object  shining  as  a  star  of  the  eighth  magnitude  not 
far  from  the  position  of  the  missing  one.  On  ,the  fol- 


ASTRONOMY.  163 

lowing  night  the  place  of  this  star  was  sensibly  altered. 
Piazzi  regarded  this  object  as  a  comet,  and  announced 
its  discovery  as  such  on  the  24th  of  January.  On  the 
publication  of  the  whole  series  of  positions  observed  at 
Palermo,  Professor  Gauss  of  Gottingen  undertook  the 
determination  of  the  orbit  of  Piazzi's  star,  and  announced 
that  it  revolved  round  the  sun  at  a  mean  distance  of 
2.7  times  the  distance  of  the  earth.  This  distance  agree- 
ing so  closely  with  that  indicated  by  Bode's  law  for  the 
planet  supposed  to  exist  between  Mars  and  Jupiter,  as- 
tronomers were  very  soon  led  to  regard  Piazzi's  comet 
as  in  reality  a  new  planet,  fulfilling,  in  a  remarkable  man- 
ner, the  condition,  in  respect  to  distance  from  the  sun, 
which  had  been  found  to  hold  good  for  the  other  mem- 
bers of  the  planetary  'system.  This  new  planet  was 
named  Ceres.  Its  minuteness  has  prevented  any  exact 
determination  of  its  diameter.  Sir  William  Herschel's 
measurement  makes  it  one  hundred  and  sixty-three  miles 
in  diameter.  Observers  have  remarked  a  haziness  sur- 
rounding the  planet,  which  is  attributed  to  the  density 
and  extent  of  its  atmosphere.  Ceres  is  generally  just 
beyond  the  range  of  unaided  vision,  though  it  has  been 
seen  without  the  telescope. 

140.  The  Discovery  of  Pallas.  —  In  order  to  find  Ceres 
more  readily,  Dr.  Olbers  examined  minutely  the  configu- 
ration of  the  small  stars  lying  near  her  path.  On  the 
28th  of  March,  1802,  after  observing  the  planet,  he  swept 
with  his  telescope  over  the  north  wing  of  Virgo,  and  was 
astonished  to  .find  a  star  of  the  seventh  magnitude,  where 
he  was  certain  no  star  was  visible  in  January  and  February 
preceding.  In  the  course  of  three  hours  he  found  that  the 
right  ascension  and  declination  of  the  star  had  changed. 
On  the  follovring  evening  he  found  the  star  had  moved 
considerably,  and  he  became  convinced  t'iat  it  was  a 
planet.  He  named  this  new  body  Pallas.  Its  orbit  was 


164  ASTRONOMY* 

soon  determined  by  Professor  Gauss,  who  found  that  its 
most  remarkable  peculiarity  consisted  in  the  great  in- 
clination of  its  plane  to  the  ecliptic.  This  inclination  is 
34°,  while  that  of  Mercury,  which  is  the  greatest  among 
the  larger  planets,  is  only  7°.  Its  mean  distance  from  the 
sun  was  found  to  be  nearly  the  same  as  that  of  Ceres. 

Dr.  Olbers  showed  that  the  orbits  of  the  newly  discov- 
ered planets  approached  very  near  each  other  at  the  as- 
cending node  of  Pallas,  a  circumstance  which  led  him 
to  make  his  remarkable  conjecture  as  to  the  common 
origin  of  these  bodies.  He  thought  that  a  much  larger 
planet  had,  in  remote  ages,  existed  near  the  mean  dis- 
tance of  Ceres  and  Pallas  ;  that,  by  some  tremendous 
catastrophe,  this  body  had  been  shattered  ;  and  that  the 
two  small  planets  were  among  the  fragments.  This  hy- 
pothesis seemed  to  be  materially  strengthened  by  subse- 
quent discoveries,  though  it  is  now  generally  admitted  to 
be  without  foundation.  The  diameter  of  Pallas  seems 
to  be  about  600  miles. 

141.  The  Discovery  of  Juno.  —  In  1804  Professor  Har- 
ding, of  Lilienthal,  while  preparing  a  chart  of  the  small 
stars   lying  near  the  paths  of  Ceres  and  Pallas,  with  a 
view  to  assist  the  identification  of  these  minute  bodies, 
discovered  a  small  object  which  he  recognized  as  a  planet 
by  its  movement.     This  planet  he  named  Juno. 

142.  The  Discovery  of  Vesta.  —  Dr.  Olbers,  following  up 
his  idea  respecting  the  origin  of  this  zone  of  planets,  con- 
sidered, from  the  fact  that  the  orbits  of  the  three  already 
found  intersect  one  another  in  Virgo  and  Cetus,  that  the 
explosion  must  have  taken  place  in  one  or  the  other  of 
those   regions,   and   consequently  that   all  the   fragments 
should   pass   through    them.     Provided  with  an   ordinary 
night  glass,  he  examined  every  month  the  small  stars  of 
Virgo  and  of  Cetus,   according  as  the  one  or  the  other 
of  these   constellations  was  the  more  favorably  situated 


ASTRONOMY.  165 

for  observation.  In  1807  he  discovered  a  small  star  in 
Virgo,  where  there  had  been  none  on  a  previous  exami- 
nation, and  he  soon  satisfied  himself  that  the  star  was 
really  in  motion,  and  thus  recognized  it  as  a  planet.  This 
planet  was  named  Vesta.  Its  diameter  is  about  300  miles. 
Dr.  Gibers  continued  his  systematic  examination  of  the 
small  stars  of  Virgo  and  Cetus  between  the  years  1808 
and  1816,  and  was  so  closely  on  the  watch  for  a  moving 
body,  that  he  considered  it  highly  improbable  that  a  planet 
could  have  passed  through  either  of  these  regions  in  the 
interval  without  detection.  No  further  discovery  being 
made,  the  plan  was  relinquished  in  1816. 

143.  More  Recent  Discoveries  of  Minor  Planets.  —  After 
Dr.  Olbers  discontinued  his  search  for  planets,  the  subject 
appears   to  have  attracted  little  attention  until   Hencke, 
an  amateur  astronomer,  took  up  the  search  with  a  zeal 
and  diligence  which  could  hardly  fail  in  producing  some 
important  result,  and  he  was  rewarded  in  1845  by  the  dis- 
covery of  a  fifth  planet,  which  was  named  Astrcea,  and  in 
1847  by  the  discovery  of  Hebe.     Since  1845  tne  discovery 
of  these  bodies  has  been  very  frequent,  and  their  number 
has  now  reached  95. 

144.  The  Group  of  Minor  Planets.  — There  is,  then,  be- 
tween Mars  and  Jupiter,  a  group  of  minute  planets,  spread 
through  a  zone  some  50,000,000  miles  in  diameter.     Their 
orbits  are  generally  more  flattened  than  those  of  the  larger 
planets,  and  their  planes  are  more  inclined  to  the  ecliptic  ; 
though  they  differ  greatly  in  this  respect,  since  the  orbits 
of  some  of  them  nearly  coincide  with  the  ecliptic.     There 
is  good  reason  to  suppose  that  many  more  will  be  dis- 
covered. 

These  planets  are  often  called  asteroids  (star-like  bodies). 


1 66  ASTRONOMY. 


SUMMARY  OF  THE  MINOR  PLANETS. 

Kepler  suspected  the  existence  of  an  unknown  planet 
between  Mars  and  Jupiter.  The  discovery  of  Uranus  in 
1781  led  the  German  astronomers  to  undertake  a  syste- 
matic search  for  this  suspected  body.  They  were  guided 
by  Bode's  law  of  planetary  distances.  (138.) 

In  1801  Pipzzi  discovered  Ceres,  but  supposed  it  to  be  a 
comet.  Professor  Gauss  showed  it  to  be  a  planet,  and  that 
it  is  at  about  the  distance  from  the  sun  required  by  Bode's 
law.  (139.) 

In  1802  Dr.  Olbers  discovered  Pallas,  The  marked 
peculiarity  of  this  planet  is  the  great  inclination  of  its  orbit 
to  the  plane  of  the  ecliptic.  Since  near  the  ascending 
node  of  Pallas  the  orbit  of  this  planet  and  of  Ceres  very 
nearly  coincide,  Dr.  Olbers  was  led  to  believe  that  Ceres 
and  Pallas  were  the  fragments  of  a  broken  planet.  (140.) 

In   1804  Juno  was  discovered  by  Harding.    (141.) 

Dr.  Olbers  now  began  a  systematic  search  for  other 
fragments  of  his  broken  planet.  In  1807  he  discovered 
Vesta.  He  continued  his  search  till  1816  without  further 
fruit.  (142.) 

No  more  of  these  minute  planets  were  discovered  till 
1845,  when  Hencke  discovered  Astraa.  In  1847  ne  dis- 
covered Hebe.  Since  that  time  these  bodies  have  been 
discovered  with  considerable  frequency.  Their  number 
now  reaches  95.  Astronomers  do  not  now  believe  that 
these  bodies  are  fragments  of  a  broken  planet.  (143-) 

The  Minor  Planets  form  a  well-marked  group.     (144.) 


ASTRONOMY.  167 


JUPITER. 

145.  Its  Distance,  Period,  Size,  etc.  —  From  the  regions 
of  space  where  we  have  just  seen  the  smallest  members 
of  our  system  moving  in  their  orbits,  we  pass  abruptly  to 
a  group  of  planets  of  a  very  different  order.  The  first 
planet  of  this  group  is  Jupiter. 

To  the  naked  eye,  Jupiter  appears  as  a  Star  of  the  first 
magnitude,  the  brightness  of  which  is  sometimes  sufficient 
to  cast  a  shadow.  It  is  the  most  brilliant  of  the  planets 
except  Venus. 

The  mean  distance  of  this  planet  from  the  sun  is 
496,000,000  miles.  He  moves  in  an  orbit  which  differs 
considerably  from  a  circle,  so  that  his  distance  from  the 
sun  at  aphelion  is  about  48,000,000  miles  greater  than 
at  perihelion.  Of  course  the  difference  of  his  distance 
from  the  earth  at  conjunction  and  opposition  is  still 
greater.  He  completes  a  revolution  in  about  twelve 
years. 

The  plane  of  Jupiter's  orbit  very  nearly  coincides  with 
that  of  the  ecliptic,  being  inclined  to  it  by  an  angle  of  a 
little  over  i°. 

The  diameter  of  Jupiter  is  about  89,000  miles,  or  about 
eleven  times  the  diameter  of  the  earth.  The  bulk,  there- 
fore, of  this  immense  planet  is  about  1400  times  that 
of  our  globe.  If  seen  at  the  distance  of.  our  satellite, 
his  disc  would  cover  a  space  in  the  sky  1200  times  that 
occupied  by  the  disc  of  the  full  moon.  Yet  this  mass  is 
travelling  through  space  with  a  velocity  about  eighty  times 
that  of  a  cannon  ball. 

Jupiter,  like  the  earth,  is  not  a  perfect  sphere,  but  an 
ellipsoid  flattened  at  the  poles.  This  flattening  is  much 
greater  than  in  the  case  of  the  earth. 

As   has   already   been   stated   (77),    Jupiter   is   accom- 


1 68  ASTRONOMY. 

panied  by  four  satellites.  These  appear  in  the  telescope 
as  so  many  points  of  light  oscillating  in  short  periods 
across  the  planet 

146.  Its  Physical  Characteristics. — On  examining  the 
surface  of  Jupiter  with  a  telescope,  we  see  no  appearance 
of  regular  continents  or  seas,  as  on  the  surface  of  Mars  ; 
but  daik  streaks,  or  belts,  are  found  to  cross  his  disc,  pre- 
senting some  of  the  modifications  of  clouds  in  our  own 
atmosphere.  Occasionally  these  belts  retain  nearly  the 
same  form  and  position  for  months  together,  while  at 
other  times  they  undergo  great  and  sudden  changes,  and, 
in  one  or  two  instances,  have  been  observed  to  break  up 
and  spread  themselves  over  the  whole  disc  of  the  planet. 
Generally  there  are  two  belts  much  more  strongly  marked 
than  the  rest,  and  more  nearly  permanent  in  their  charac- 
ter, one  situated  a  little  north  and  the  other  a  little  south 
of  the  planet's  equator.  The  prevailing  opinion  among 
astronomers  is  that  these  phenomena  are  produced  by  dis- 
turbances in  the  planet's  atmosphere,  which  occasionally 
render  its  dark  body  visible ;  and  as  the  belts  are  found 
to  traverse  the  disc  in  lines  uniformly  parallel  to  Jupiter's 
equator,  (see  Figure  69,)  we  are  naturally  led  to  the 
conclusion  that  these  disturbances  are  connected  with  the 
rotation  of  the  planet  on  its  axis,  in  the  same  way  that  the 
trade  winds  on  the  earth  are  connected  with  its  rotation 
on  its  axis. 

In  July,  1665,  Cassini,  of  Paris,  remarked  a  black  spot 
of  considerable  apparent  magnitude  on  the  upper  edge 
of  the  southern  belt  of  Jupiter,  which  remained  visible 
two  years.  This  spot,  or  one  supposed  to  be  identical 
with  it,  has  repeatedly  appeared  since  that  time,  but  at 
very  irregular  intervals. 

In  1834,  a  remarkable  spot  was  discovered  on  the  north- 
ern belt.  It  was  black  and  well  defined  ;  about  two  thirds 
of  its  breadth  was  above  the  belt,  and  one  third  upon  it. 


ASTRONOMY.  169 

Fig.  69. 


Shortly  after  this  spot  was  first  noticed  a  second  distinct 
spot  was  discovered  on  the  same  belt.  These  spots  re- 
mained wholly  unchanged  for  nearly  a  year.  Cassini  no- 
ticed that  the  spot  of  1665  appeared  to  traverse  the  disc  of 
the  planet  from  east  to  west.  It  was  very  conspicuous  near 
the  centre  of  the  disc,  but  gradually  faded  away  as  it  ap- 
proached the  western  limb.  The  motion  seemed  quickest 
when  the  spot  was  near  the  centre",  and  became  slower 
towards  the  edge  of  the  planet.  Hence  he  inferred  that 
the  spot  adhered  to  the  surface  of  the  planet,  and  was  car- 
ried across  the  disc  by  the  rotation  of  Jupiter  upon  his 
axis.  This  hypothesis  would  account  fully  for  the  ap- 
pearances observed.  By  closely  watching  the  movements 
of  the  spot,  Cassini  ascertained  that  the  time  of  rotation 
of  the  planet  was  9  hours  56  minutes. 

By  careful  observations  of  the  spots  of  1834  the  time 

of  rotation   was  found  to  be  about  half  a  minute   less. 

This    enormous   globe,    whose   diameter   is    eleven   times 

greater  than  that  of  the  earth,  is  therefore  whirled  upon 

8 


1 70  ASTRONOMY. 

its  axis  in  less  than  ten  hours.     The  axis  of  rotation  is 
very  nearly  perpendicular  to  the  plane  of  the  orbit. 

147.  The  Satellites  of  Jupiter.  —  These  bodies  were  dis- 
covered by  Galileo   in    1610.     They  shine  with  the  bril- 
liancy of  stars  between  the  sixth  and  seventh  magnitude  ; 
but  owing  to  their  proximity  to  the  planet  they  are  invisi- 
ble to  the  naked  eye. 

Their  configuration  is  continually  changing.  Sometimes 
they  are  all  situated  on  one  side  of  the  planet,  though 
more  often  one  at  least  is  found  on  each  side.  In  very 
rare  instances  all  four  have  been  invisible,  as  on  the  2ist 
of  August,  1867,  when  the  planet  appeared  thus  unattend- 
ed for  one  hour  and  three  quarters.  It  is  not  a  rare  oc- 
currence to  find  only  one  satellite  visible. 

Sir  William  Herschel,  from  a  long  series  of  observa- 
tions on  the  satellites,  concluded  that  they  rotate  on 
their  axis  in  the  time  of  one  synodical  revolution  around 
Jupiter,  thus  presenting  an  analogy  to  our  own  satellite. 
He  was  led  to  this  conclusion  on  remarking  the  great 
changes  in  the  relative  brightness  of  the  satellites  in 
different  positions,  which  were  found  to  follow  such  a 
law  as  could  be  reconciled  only  with  this  hypothesis. 

148.  The  Eclipses  of  these  Satellites.  —  If  Jupiter   were 
a  self-luminous  body,  the  satellites  would  disappear  only 
when  they  pass  behind  him.     But  they  disappear  at  other 
times  and  in  such  a  way  as  to  show  that  the  planet  must 
be  an  opaque,  non-luminous  body.     This  will  be  seen  by 
reference  to  Figure  70. 

If  Jupiter  be  non-luminous,  he  will  cast  a  shadow  di- 
rectly away  from  the  sun,  as  shown  in  the  figure.  The 
satellites  will  then  disappear,  not  only  when  they  pass 
behind  the  planet  (as  in  the  case  of  the  satellites  m  and 
m  "  when  the  earth  is  at  E\  but  also  when  they  pass 
through  the  shadow  of  the  planet  (as  in  the  case  of  m 
when  the  earth  is  at  E') ;  and  this  they  are  found  to  do. 


ASTRONOMY. 
Fig.  70. 


171 


When  they  disappear  behind  the  planet  they  are  occulted ; 
when  they  pass  through  the  shadow  they  are  eclipsed. 
The  entrance  of  the  satellite  into  the  shadow  is  called 
its  immersion,  and  its  exit  from  the  shadow  its  emersion. 
The  shadow  is  sometimes  so  projected  that  both  the  im- 
mersion and  emersion  of  the  satellite  can  be  seen,  and 
at  other  times  so  that  only  one  of  them  can  be  seen. 
Three  of  the  satellites  are  totally  eclipsed  at  every  revolu- 
tion, while  the  fourth  is  often  only  partially  eclipsed,  or 


172  ASTRONOMY. 

not  eclipsed  at  all,  since  its  orbit  is  inclined  to  the  orbit 
of  Jupiter  by  a  greater  angle  than  that  of  the  others. 

When  a  satellite  passes  between -us  and  Jupiter  it  makes 
a  transit  across  his  disc.  As  seen  by  the  rigure  the  shad- 
ow of  the  satellite,  as  m ',  is  often  projected  on  the  disc  at 
a  different  place  from  the  satellite  itself.  The  shadow 
always  appears  as  a  round  black  spot  upon  the  disc,  while 
the  satellite  usually  appears  as  a  bright  spot,  often  brighter 
than  the  general  disc  of  Jupiter.  They  have,  however, 
been  observed  as  dark  spots,  a  phenomenon  which  can  be 
accounted  for  only  by  supposing  that  such  spots  really 
exist  on  the  satellites  themselves,  for  their  illuminated  face 
must  be  turned  towards  us  at  the  time. 


SATURN. 

149.  Distance,  Period,  Size,  etc.  —  The  next  planet  in 
the  order  of  distance  from  the  sun  is  Saturn,  who  per- 
forms his  revolution  in  about  29^  years,  at  a  mean  dis- 
tance of  909,000,000  miles  from  the  sun,  in  an  orbit  con- 
siderably flattened,  and  inclined  to  the  ecliptic  at  an  angle 
of  about  2-J  degrees. 

The  diameter  of  Saturn  is  found  to  be  about  73,000 
miles,  or  about  nine  times  that  of  the  earth.  The  bulk  of 
Saturn  is  consequently  about  eight  hundred  times  that  of 
the  earth. 

Though  belts  are  frequently  observed  with  good  tele- 
scopes on  the  surface  of  Saturn,  they  are  much  less  dis- 
tinct than  those  of  Jupiter.  Spots  are  of  rare  occurrence. 
One  was  seen  by  Sir  William  Herschel  in  1780  for  several 
days,  and  another  quite  distinct  was  seen  in  1847. 

In  1793,  Sir  W.  Herschel  saw  a  quintuple  belt.  By 
very  frequent  and  careful  examination  of  the  appearance 
of  this  belt  he  ascertained  that  the  time  of  rotation  of 
Saturn  is  a  little  over  ten  hours. 


ASTRONOMY.  173 

The  axis  of  rotation  is  inclined  to  the  plane  of  the 
planet's  orbit  at  an  angle  of  about  63°.  His  seasons  are 
therefore  more  diversified  than  those  of  Jupiter. 

150.  The  Satellites  and  the  Rings  of  Saturn.  —  Though 
Saturn  is  smaller  than  Jupiter,  his  system  is  far  more  com- 
plicated. He  is  attended  by  eight  satellites.  While  the 
satellites  of  Jupiter  are  known  respectively  as  the  first, 
second,  third,  and  fourth,  those  of  Saturn  have  mythologi- 
cal names.  Their  names  in  the  order  of  distance  are 
Mimas,  Enceladus,  Tethys,  Dione,  Rhea,  Titan,  Hype- 
rion, and  Japetus.  Of  these  Titan  is  the  largest.  But 
the  most  interesting  feature  of  the  Saturnian  system  is  his 
rings. 

When  Galileo  turned  his  newly  constructed  telescope 
upon  Saturn,  he  saw  that  the  figure  of  the  planet  was  not 
round  as  in  the  case  of  Jupiter.  At  first  he  thought  it  to 
be  oblong,  but  on  further  examination  he  concluded  that 
the  planet  consisted  of  a  large  globe,  with  a  smaller  one 
on  each  side  of  it.  Continuing  his  observation  he  re- 
marked that  this  appearance  was  not  constantly  the 
same,  the  appendages  on  each  side  of  the  central  globe 
gradually  diminishing  until  they  vanished  entirely,  and  left 
the  planet  nearly  round,  without  anything  extraordinary 
about  it.  He  therefore  concluded  that  he  had  been 
mocked  by  an  optical  illusion. 

Huyghens,  who  possessed  telescopes  of  greater  power 
than  those  of  the  Italian  astronomer,  was  the  first  who 
gave  a  correct  explanation  of  these  varied  appearances, 
and  detected  a  luminous  ring  surrounding  the  globe  of 
Saturn.  In  1675,  Cassini  discovered  a  division  separat- 
ing the  ring  into  two  concentric  rings.  This  division  had 
been  detected  ten  years  previously  by  two  English  ama- 
teurs. 

The  ring  of  Saturn  may  be  described  as  broad  and 
flat,  situated  exactly  in  the  plane  of  the  planet's  equator, 


174 


ASTRONOMY. 


an  .1  consequently  inclined  to  the  ecliptic  at  an  angle  of 
about  28°.  It  keeps  this  same  inclination  throughout  the 
revolution  of  Saturn.  The  plane  of  the  ring  therefore 
intersects  the  ecliptic.  It  is  owing  to  this  inclination 
that  the  ring  is  sometimes  observed  as  a  broad  ellipse, 


at  other  times  as  a  straight  line  barely  discernible  with 
the  most  powerful  telescopes,  and  that  at  other  times  the 
ring  entirely  disappears.  These  phases  of  the  ring  will 
be  understood  by  reference  to  Figure  71. 

In  two  positions  of  the  planet  the  plane  of  the  ring  is 
seen  to  pass  through  the  centre  of  the  sun,  and  of  course 


ASTRONOMY.  1 75 

only  its  edge  is  illumined.  Now  the  ring  is  estimated  to 
be  about  one  hundred  miles  thick.  This  thickness,  at  the 
distance  of  Saturn,  .would  subtend  an  angle  just  about 
equal  to  that  of  a  good-sized  pin  at  the  distance  of  two 
miles.  Hence  in  these  two  positions  the  ring  will  appear 
as  a  line  of  light  discernible  only  with  the  most  powerful 
telescopes.  Suppose  that  some  time  before  the  ring  came 
into  the  position  marked  1848  the  earth  was  at  A  :  then 
the  plane  of  the  ring  would  pass  between  the  earth  and 
the  sun,  and  the  unillumined  side  of  the  ring  would  be 
turned  towards  us,  and  the  ring  would  of  course  disap- 
pear. So,  too,  if  some  time  after  the  ring  came  into  this 
position  the  earth  were  at  B,  the  plane  of  the  ring  would 
again  pass  between  the  earth  and  the  sun,  and  the  ring 
would  again  disappear.  At  the  positions  marked  1855 
and  1869,  the  ring  would  appear  as  a  broad  ellipse. 

More  recent  observations  go  to  show  that  the  two  di- 
visions of  Saturn's  ring  are  further  subdivided,  so  as  to 
constitute  a  multiple  ring. 

The  most  recent,  and  at  the  same  time  one  of  the  most 
remarkable  discoveries  with  reference  to  the  rings  of 
Saturn,  is  that  of  a  dusky  or  obscure  ring,  nearer  to  the 
planet  than  the  intensely  bright  one.  This  dusky  ring 
seems  to  have  been  first  noticed  by  Dr.  Galle  of  Berlin, 
but  this  notice  attracted  but  little  attention  till  1850,  when 
the  phenomenon  was  remarked  by  Prof.  Bond,  of  Cam- 
bridge, Mass.,  and  by  Mr.  Dawes,  of  England.  The  latter 
detected  a  division  of  the  obscure  ring. 

This  newly  discovered  ring  is  quite  transparent,  allowing 
the  disc  of  the  planet  to  be  seen  through  it. 

Fig.  72  represents  Saturn  with  his  system  of  rings. 

When  the  ring  last  appeared,  as  a  mere  line,  in  1861 
and  1862,  singular  appendages,  like  clouds  of  less  intense 
light,  were  noticed  lying  on  each  side  of  the  ring. 

The  ring  of  Saturn  has  been  supposed  to  be  solid,  and 


to  be  liquid;  and  able  mathematicians  have  in  turn  de- 
monstrated that  it  can  be  neither.  It  is  now  held  by  some 
that  it  is  composed  of  innumerable  little  satellites  revolv- 
ing about  the  planet,  in  the  plane  of  his  equator. 

The  system  of  rings  seems  to  be  increasing  in  breadth 
at  the  rate  of  about  twenty-nine  miles  a  year. 

URANUS. 

151.  Its  Discovery.  —  Previous  to  the  year  1781,  the  only 
planets  known,  beside  the  one  we  inhabit,  were  Mercury, 
Venus,  Mars,  Jupiter,  and  Saturn.  All  of  these  are  more 
or  less  conspicuous  to  the  naked  eye,  and  were  recognized 


ASTRONOMY.  177 

from  the  earliest  antiquity  as  wandering  bodies.  Saturn 
was  supposed  to  be  the  most  distant  member  of  the  solar 
system,  and  very  little  suspicion  of  the  existence  of  an 
exterior  planet  was  entertained.  The  close  examination 
of  the  heavens,  begun  by  Sir  William  Herschel  in  1781, 
led  to  a  discovery  which  more  than  doubled  the  area  of 
our  system. 

On  the  i3th  of  March,  1781,  while  exploring  with  his 
telescope  the  constellation  of  the  Twins,  he  observed  a 
star,  the  disc  of  which  attracted  his  attention.  Perceiving, 
after  a  few  nights  of  observation,  that  the  new  body  moved, 
he  at  first  mistook  it  for  a  comet ;  but  it  soon  became  evi- 
dent that  it  was  a  new  planet,  outside  the  orbit  of  Saturn. 

152.  Its  Period,  Distance,  Size,  etc.  —  This  planet  may 
just  be   discerned   by  a  person   of  very  good   eyesight, 
without  a  telescope.     Uranus  revolves  about  the  sun  in  a 
period  of  about  eighty-four  years,  at  a  mean  distance  of 
1,828,000,000  miles,  in  an  elliptical  orbit,  whose  plane  is 
inclined  to  the  ecliptic  at  an  angle  of  less  than  i°.     Its 
diameter  is  about  36,000  miles. 

No  telescopes  hitherto  constructed  have  succeeded  in 
showing  any  spots  or  belts  upon  this  planet,  owing  to  its 
enormous  distance  and  the  consequent  minuteness  of  its 
disc.  The  time  of  its  rotation,  and  the  position  of  its 
axis  with  respect  to  the  plane  of  its  orbit,  are,  therefore, 
unknown,  and  are  likely  to  remain  so. 

153.  Its  Satellites.  —  Sir  William  Herschel.  thought  he 
had  detected  six  satellites  of  this  planet,  but  it  is  now 
pretty  well  established  that  there  are  but  four.     It  is  a 
curious  fact  that  the  satellites  of  Uranus,  unlike  those  of 
the  earth,  Jupiter,  and  Saturn,  revolve  in  a  retrograde  direc- 
tion, —  that  is,  from  east  to  west,  —  and  that  their  orbits 
are  inclined  at  a  very  large  angle  to  that  of  the  planet. 

8*  L 


178  ASTRONOMY. 


NEPTUNE. 

154.  Its  Period,  Distance,  Size,  etc.  —  The  next  planet  in 
the  order  of  distance  from  the  sun,  and,  so  far  as  we  know, 
the  last  of  the  solar  system,  is  Neptune.     He  revolves 
around  the  sun  in  a  period  of  164  years,  at  a  mean  dis- 
tance of  2,862,000,000  miles,  in  an  orbit  inclined  to  the 
ecliptic  at  an  angle  of  a  little  less  than  2°.     His  diameter 
is  about  35,000  miles.     No  spots  can  be  detected  on  his 
disc,  and  consequently  nothing  is  known  about  his  time  of 
rotation  or  the  inclination  of  his  axis.     He  is  certainly  at- 
tended by  one  satellite,  which,  like  those  of  Uranus,  moves 
in  a  retrograde  direction. 

155.  Its  Discovery.  —  Though  we  know  so  little  of  this 
most  distant  member  of  our  system,  yet  the  circumstances 
of  its  discovery  give  it  an  enduring  interest. 

It  will  be  shown,  further  on,  that  the  planets,  by  their 
mutual  action,  disturb  one  another's  orbits  to  a  slight  ex- 
tent, so  that  none  of  them  describe  exact  ellipses.  It  had 
been  noticed  for  many  years  that  the  motion  of  Uranus 
was  not  exactly  what  it  was  calculated  it  should  be,  after 
making  allowance  for  all  known  causes  of  disturbance. 
Two  young  mathematicians,  M.  Le  Verrier,  of  France,  and 
Mr.  Adams,  of  England,  were  led,  unknown  to  each  other, 
to  inquire  into  the  cause  of  this  apparent  anomaly,  and 
both  soon  came  to  the  conclusion  that  a  planet  of  consid- 
erable magnitude  must  exist  outside  the  orbit  of  Uranus. 
Their  next  object  was  to  ascertain  the  position  of  the 
planet  amongst  the  stars,  with  a  view  to  its  actual  discov- 
ery in  the  telescope ;  but  the  problem  to  be  solved  was 
one  of  excessive  difficulty,  —  so  much  so,  in  fact,  that  sev- 
eral of  the  most  eminent  astronomers  had  declared  their 
conviction  that  the  place  of  the  latent  planet  could  never 
be  discovered  by  calculation.  M.  Le  Verrier  and  Mr. 


ASTRONOMY.  179 

Adams  were  of  a  different  opinion,  and  finally  succeeded  in 
their  researches,  which  assigned  nearly  the  same  position 
to  the  body  whose  influence  had  been  so  visibly  exercised 
on  the  movements  of  Uranus.  Mr.  Adams,  however,  did 
not  make  his  conclusions  public  through  the  press,  and 
much  of  the  first  glory  of  this  great  discovery  was  conse- 
quently given  to  the  French  astronomer,  who  had  an- 
nounced the  position  of  the  new  planet  to  the  Academy 
of  Sciences  at  Paris  in  the  summer  of  1846.  On  the  23d 
of  September,  of  the  same  year,  Dr.  Galle,  of  the  Royal 
Observatory,  Berlin,  acting  upon  the  urgent  representa- 
tions of  M.  Le  Verrier,  contained  in  a  letter  which  reached 
Berlin  at  this  date,  turned  the  large  telescope  of  the 
observatory  to  that  part  of  the  heavens  in  which  M.  Le 
Verrier  had  informed  him  he  would  find  the  disturbing 
planet.  Hardly  was  this  done  when  a  pretty  bright  tele- 
scopic star  appeared  in  the  field  of  view,  at  a  point  where 
no  such  object  was  marked  in  a  carefully  prepared  map 
of  that  part  of  the  heavens.  This  proved  to  be  the  pre- 
dicted planet,  and  the  name  Neptune  was  given  to  it  by  the 
common  consent  of  M.  Le  Verrier,  Mr.  Adams,  and  the 
chief  astronomers  of  Europe. 

In  calculating  the  position  of  this  planet,  they  had  as- 
sumed, according  to  Bode's  law,  that  it  would  be  about 
twice  as  distant  as  Uranus.  But  the  mean  distance  of 
Neptune  is  found  to  be  considerably  less  than  double  that 
of  Uranus ;  hence  this  law,  which  led  to  the  discovery  of 
minor  planets,  and  helped  in  the  discovery  of  Neptune,  has 
singularly  enough  been  overthrown  by  these  discoveries. 

156.  The  Outer  Group  of  Planets.  —  The  third  outer 
group  of  planets  comprises  the  large  bodies  outside  the 
ring  of  telescopic  planets.  Jupiter,  Saturn,  Uranus,  and 
Neptune  belong  to  this  group.  So  far  as  known,  they 
rotate  in  periods  of  about  ten  hours,  and  three  of  them 
at  least  are  attended  by  a  number  of  satellites.  They 
have  also  a  very  slight  density. 


l8o  ASTRONOMY. 


SUMMARY  OF  THE  OUTER  GROUP  OF 
PLANETS. 

The  first  and  largest  planet  of  this  group  is  Jupiter. 
His  diameter  is  about  eleven  times  that  of  the  earth. 
He  completes  a  revolution  in  about  twelve  years,  and  is 
attended  by  four  satellites.  (144.) 

The  disc  of  Jupiter  is  crossed  by  a  number  of  parallel 
belts,  which  sometimes  resemble  clouds.  The  most  strong- 
ly marked  of  these  are  situated  near  the  equator  of  the 
planet.  They  are  probably  due  to  a  disturbance  in  Ju- 
piter's atmosphere  analogous  to  our  trade  winds.  By  ob- 
servation of  certain  well-marked  spots  Jupiter  has  been 
found  to  rotate  on  his  axis  in  a  little  less  than  ten  hours. 

(145.) 

The  satellites  of  Jupiter  were  first  discovered  in  1610. 
They  are  occulted  when  they  pass  behind  the  planet ; 
eclipsed  when  they  pass  into  its  shadow  ;  and  make  tran- 
sits across  the  planet's  disc  when  they  pass  between  it 
and  the  sun.  At  rare  intervals  Jupiter  is  seen  without 
satellites.  (146,  147.) 

The  next  planet  of  this  group  is  Saturn.  He  is  not  so 
large  as  Jupiter,  his  diameter  being  but  nine  times  that  of 
the  earth.  He  completes  a  revolution  in  about  29 \  years. 
He  has  belts,  but  they  are  less  marked  and  less  perma- 
nent than  those  of  Jupiter.  He  is  found  to  rotate  on  his 
axis  in  about  ten  hours.  (148.) 

Saturn  is  attended  by  eight  satellites,  and  by  a  most  re- 
markable system  of  rings.  These  rings  are  parallel  to  the 
plane  of  the  planet's  equator,  and  inclined  to  that  of  its 
orbit  at  an  angle  of  about  28°.  It  is  owing  to  this  in- 
clination that  the  rings  sometimes  appear  as  broad  ellipses, 
and  at  other  times  as  mere  straight  lines.  The  rings 
occasionally  disappear  entirely.  Little  is  known  of  the 


ASTRONOMY.  l8l 

physical  constitution  of  these  rings.  They  are  certainly 
several  in  number,  and  appear  to  be  slowly  increasing 
in  breadth.  (149.) 

Mercury,  Venus,  Mars,  Jupiter,  and  Saturn  are  the  only 
planets  visible  to  the  naked  eye,  and  up  to  the  year  1781, 
they  were  the  only  ones  known  to  exist  In  that  year 
Herschel  announced  the  discovery  of  a  new  planet,  since 
named  Uranus.  (150.) 

Uranus  is  about  twice  as  distant  as  Jupiter,  and  his 
diameter  is  about  five  times  that  of  the  earth.  He  com- 
pletes a  revolution  in  about  84  years,  but  nothing  is  known 
about  his  rotation  on  his  axis.  (151.) 

He  is  attended  by  at  least  four  satellites,  all  of  which 
have  a  retrograde  motion.  (152.) 

The  last  member  of  this  group,  and,  so  far  as  we  know, 
of  our  planetary  system,  is  Neptune.  His  disc  is  about 
the  same  as  that  of  Uranus.  He  completes  a  revolution 
in  about  164  years,  while  nothing  is  known  about  his 
rotation.  Neptune  is  attended  by  one  satellite,  which  has 
a  retrograde  motion.  (153.) 

A  peculiar  interest  attaches  itself  to  this  remote  body, 
owing  to  the  circumstances  of  its  discovery.  (154.) 

The  planets,  so  far  as  known,  all  rotate  on  their  axes 
from  west  to  east.  They  also  revolve  about  the  sun  from 
west  to  east,  while  the  satellites,  with  the  exception  of 
those  of  Uranus  and  Neptune,  revolve  about  their  pri- 
maries from  west  to  east.  The  sun  and  moon  also  rotate 
from  west  to  east. 

COMETS. 

157.  There  is  another  group  of  well-known  bodies 
called  Comets,  which  differ  in  so  many  respects  from 
the  planets  that  they  seem  hardly  to  belong  to  the  same 
system. 


1 82  ASTRONOMY. 

These  bodies  are  observed  only  in  those  parts  of  their 
orbits  which  are  nearest  to  the  sun.  They  are  not  con- 
fined, like  the  larger  planets,  to  the  zodiac,  but  appear  in 
every  quarter  of  the  heavens,  and  move  in  every  possible 
direction.  They  usually  continue  visible  a  few  weeks  or 
months,  and  very  rarely  so  long  as  a  year.  Their  ap- 
pearance, with  some  few  exceptions,  is  nebulous  or  cloud- 
like,  whence  it  is  inferred  that  they  consist  of  masses  of 
vapor,  though  in  a  highly  attenuated  state,  since  very- 
small  stars  are  often  seen  through  them. 

The  more  conspicuous  comets  are  accompanied  by  a 
tail,  or  train  of  light,  which  sometimes  stretches  over  an 
arc  of  the  heavens  of  50°  or  upwards,  but  more  fre- 
quently is  of  much  less  extent. 

The  same  comet  may  assume  very  different  appearances 
during  its  visibility,  according  to  its  position  with  respect 
to  the  earth  and  sun.  When  first  perceptible,  a  comet 
resembles  a  little  spot  of  faint  light  upon  the  dark  ground 
of  the  sky  •  as  it  approaches  the  sun  its  brightness  in- 
creases, and  the  tail  begins  to  show  itself.  Generally  the 
comet  is  brightest  when  it  arrives  near  its  perihelion,  and 
gradually  fades  away  as  it  recedes  from  the  sun,  until  it 
cannot  be  seen  with  the  best  telescopes  we  possess. 

Some  few  have  become  so  intensely  brilliant  as  to  be 
seen  in  full  daylight.  A  remarkable  instance  of  this  kind 
occurred  in  1843,  when  a  comet  was  discovered  within 
a  few  degrees  of  the  sun  himself;  and  there  are  one  or 
two  similar  cases  on  record. 

The  brighter  or  more  condensed  part  of  a  comet,  from 
which  the  tail  proceeds,  is  called  the  nucleus ;  and  the 
nebulous  matter  surrounding  the  nucleus  is  termed  the 
coma ;  frequently  the  nucleus  and  coma  are  included  un- 
der the  general  term  head.  Some  comets  have  no  nuclei, 
their  light  being  nearly  uniform. 

The  tail  of  a  comet  is  merely  a  prolongation  of  the  neb- 


ASTRONOMY.  183 

ulous  envelope  surrounding  the  nucleus,  and  it  almost 
always  extends  in  a  direction  opposite  to  that  of  the  sun 
at  the  time.  In  some  cases  it  is  long  and  straight ;  in 
others,  curved  near  the  extremity,  or  divided  into  two 
or  more  branches.  A  few  comets  have  exhibited  two 
distinct  tails.  The  real  length  of  this  train  has  some- 
times exceeded  100  or  150  millions  of  miles  ;  that  of  the 
great  comet  of  1843  is  said  to  have  been  200  millions  of 
miles  long. 

Comparatively  few  of  the  many  comets  that  visit  our 
system  are  visible  to  the  naked  eye.  Most  of  them  are 
faint  filmy  masses,  without  tails,  which  can  be  seen  only 
with  the  telescope. 

It  is  supposed  that  the  general  form  of  the  orbits  of 
these  bodies  is  a  highly  elongated  ellipse. 

158.  ff alley's  and  other  famous  Comets.  —  Astronomers 
have  ascertained  with  great  precision  the  periods  which 
certain  comets  require  to  perform  their  revolutions  round 
the  sun,  and  are  able  to  predict  the  times  of  their  reap- 
pearance, and  their  paths  among  the  stars.  This  was  first 
done  by  Dr.  Halley,  in  the  case  of  the  comet  observed  in 
1682,  which  he  discovered  to  be  the  same  that  had  ap- 
peared in  1456,  1531,  and  1607,  and  hence  concluded 
that  its  revolution  is  accomplished  in  about  seventy- 
five  years.  He  foretold  its  reappearance  in  1759,  which 
actually  took  place  after  a  retardation  of  between  one 
and  two  years.  The  same  body  appeared  again  in  1835, 
and  will  again  visit  our  solar  system  about  the  year 
1911.  It  may  be  traced  in  history  as  far  back  as  the 
year  n  B.  C. 

A  comet  called  Encke's  has  a  period  of  3^  years; 
another,  Bielcts^  of  6f  years ;  and  several  others  perform 
their  revolutions  in  from  five  to  eight  years. 

There  are  a  few  comets,  besides  the  ones  above  men- 
tioned, which  complete  their  journey  round  the  sun  in 


184  ASTRONOMY. 

from  sixty  to  eighty  years  ;  but  it  is  certain  that  by  far 
the  greater  number  require  hundreds  or  even  thousands 
of  years  to  perform  their  revolutions.  When  this  is  the 
case,  it  becomes  almost  impossible  to  assign  their  exact 
periods. 

Remarkable  comets  appeared  in  1680  and  1843,  both 
of  which  approached  so  near  to  the  sun  as  almost  to 
graze  his  surface.  The  comet  of  1811  has  acquired  great 
celebrity.  It  remained  visible  to  the  naked  eye  several 
months,  shining  with  the  lustre  of  the  brighter  stars,  and 
attended  by  a  beautiful  fan-shaped  tail.  This  body  is 
supposed  to  require  upwards  of  3000  years  to  complete 
its  excursion  through  space. 

The  splendid  comet  of  1858,  generally  known  as  Dona- 
tfsy  will  long  be  remembered  for  the  remarkable  physical 
appearances  it  presented  in  the  telescope,  as  well  as  on 
account  of  its  imposing  aspect  to  the  naked  eye.  It  is 
presumed  to  have  a  period  of  revolution  of  about  2100 
years. 

Hardly  less  famous  in  future  times  will  be  the  grand 
comet  which  appeared  in  1861.  This  comet  had  a  tail 
100  degrees  in  length.  Its  period  of  revolution  would 
appear  to  be  much  shorter  than  that  of  Donati's  comet, 
probably  not  exceeding  450  years. 

It  is  probable  that  there  are  many  thousands  of  comets 
belonging  to  the  solar  system,  of  which  a  large  proportion 
never  come  sufficiently  near  the  sun  to  be  seen  from  the 
Earth. 

SUMMARY. 

The  comets  are  a  group  of  bodies  quite  unlike  the 
planets.  They  are  visible  only  when  near  the  sun.  They 
appear  in  every  quarter  of  the  heavens,  and  move  in  every 
possible  direction. 


ASTRONOMY.  185 

The  largest  comets  consist  of  a  nucleus,  a  coma,  and  a 
tail.  Their  trains  are  often  of  great  length.  A  comet 
usually  changes  its  appearance  •  considerably  during  its 
visibility. 

Comparatively  few  comets  are  visible  to  the  naked 
eye.  (157.) 

Several  of  the  comets  are  known  to  return  to  the  sun 
at  intervals  of  greater  or  less  length. 

Some  of  the  'most  famous  comets  are  Halley's,  which 
has  a  period  of  about  seventy-five  years ;  EnckJs,  whose 
period  is  about  three  and  a  half  years;  those  of  1680  and 
1843,  which  approached  very  near  the  sun ;  that  of  1811, 
which  remained  visible  several  months,  and  was  attended 
by  a  beautiful  fan-shaped  tail ;  Donati's,  which  is  thought 
to  have  a  period  of  about  2100  years;  and  that  of  1861, 
noted  for  the  splendor  of  its  train.  (158.) 

THE  FIXED   STARS. 

159.  We  have  already  seen  (78)  that  the  stars  are  not 
absolutely  fixed  :  many  of  them  are  known  to  be  moving 
at  the  rate  of  several  miles  a  second.     It  is  only  owing  to 
their  immense  distance  from  us  and  from  one  another  that 
their  configurations  do  no{  appear  to  change.     The  most 
noticeable  feature  of  the  fix^ed  stars  is  their  scintillation  or 
twinkling,  which  contrasts  so  strongly  with  the  steady  light 
of  the   principal   planets.      This   twinkling,  is  an   optical 
phenomenon,  supposed  to  be  due  to  what  is  termed  the 
interference  of  light.     Humboldt  states  that  in  the  pure  air 
of  Cumana,  in  South  America,  the  stars  do  not  twinkle 
after  they  attain  an  elevation,  on  the  average,  of  15°  above 
the  horizon.     Hence  we  must  conclude  that  the  twinkling 
of  the  stars  is  due  to  atmospheric  conditions. 

1 60.  Their  Number.  —  The  actual  number  of  stars  vis- 
ible to  the  naked  eye,  at  the  same  time,  on  a  clear,  dark 


1 86  ASTRONOMY. 

night,  is  between  two  and  three  thousand,  though  a  person 
forming  an  estimate  of  their  number  from  casual  observa- 
tion is  almost  certain  to  make  it  very  much  larger.  It  is  a 
well-ascertained  fact  that,  in  the  whole  heavens,  the  stars 
which  can  be  distinctly  seen  without  the  telescope,  by  any 
one  gifted  with  good  sight,  do  not  exceed  six  thousand. 

The  telescopic  -stars  are  innumerable.  It  has  been  con- 
jectured that  more  than  twenty  millions  might  be  seen  with 
one  of  Herschel's  twenty-feet  reflectors ;  and  if  we  could 
greatly  increase  the  power  of  our  telescopes,  there  is  no 
doubt  that  the  number  actually  discernible  would  be  vastly 
augmented. 

161.  Magnitudes. — The  stars  are  divided,  according  to 
their  degrees  of  brightness,  into  separate  classes,  called 
magnitudes.     The  most  conspicuous  are  termed  stars  of 
the  first  magnitude  :    there  are   about  twenty  of  these. 
The  next  in  order  of  intensity  of  light  are  stars  of  the 
second  magnitude,  which  are  about  fifty  or  sixty  in  number. 
Of  the  third  magnitude  there  are  two  hundred  or  upwards, 
and  many  more  of  the  fourth,  fifth,  and  sixth.     These  six 
classes  comprise  all  the  stars  that  can  be  well  seen  with 
the  naked  eye  on  a  clear  night.     Telescopes  in  common 
use  will  show  fainter  stars  to  the  tenth  magnitude  inclusive, 
while  the  powerful  instruments  in  observatories  reveal  an 
almost   infinite   multitude   of ,  others,   even   down   to   the 
eighteenth  or  twentieth  magnitudes. 

This  classification  of  the  stars  is,  to  a  great  degree, 
arbitrary,  so  that  it  is  not  unusual  to  find  astronomers  dif- 
fering greatly  in  their  estimates  of  brightness. 

162.  Constellations* — For  the  sake  of  more  readily  dis- 
tinguishing the  stars,  and  referring  to  any  particular  quar- 
ter of  the  heavens,  they  have  been  arranged  into  groups 
called   constellations,    each    named    from   some   object   to 
which  the  configuration  of  its  stars  may  be  supposed  to 

*  See  Appendix,  VI. 


ASTRONOMY.  187 

bear  a  resemblance.  Many  are  figures  01  heroes,  birds, 
and  animals,  connected  with  the  fables  of  classical  my- 
thology. This  mode  of  grouping  the  stars  is  of  very 
ancient  date. 

There  are  twelve  constellations  in  the  zodiac  (a  belt  of 
the  heavens  extending  8°  on  each  side  of  the  ecliptic,  and 
including  the  paths  of  all  the  larger  planets),  and  hence 
called  the  zodiacal  constellations,  viz.  Aries,  Taurus,  Gemini, 
Cancer,  Leo,  Virgo,  Libra,  Scorpio,  Sagittarius,  Capricor- 
nus,  Aquarius,  Pisces.  These  are  also  the  names  of  the 
twelve  signs,  or  divisions  of  30°  each,  into  which  the  zodiac 
was  formerly  divided;  but  the  effect  of  precession  (20), 
which  throws  back  the  place  of  the  equinox  among  the 
stars  from  year  to  year,  prevents  a  constant  agreement 
between  these  constellations  and  the  corresponding  signs. 

163.  Names  of  the  Stars.  —  Many  of  the  brighter  stars 
had  proper  names  assigned  to  them  at  a  very  early  date, 
as  Sirius,  Arcturus,  Rigel,  Aldebaran,  etc.,  and  by  these 
names  they  are  still  commonly  distinguished. 

The  stars  are  now  usually  designated  by  the  letters  of 
the  Greek  alphabet,  to  which  the  genitive  of  the  Latin 
name  of  the  constellation  is  added,  The  brightest  star  is 
called  a  (alpha),  the  next  /3  (beta),  and  so  on.  Thus,  Al- 
debaran  is  termed  a  Tauri ;  Rigel,  £  Orionis ;  Sirius,  a 
Canis  Majoris. 

164.  The  Color  of  the  Stars.  —  Many  of  the  stars  shine 
with  colored  light,  as  red,  blue,  green,  or  yellow. 

These  colors  are  exhibited  in  striking  contrast  in  many 
of  the  double  stars.  Combinations  of  blue  and  yellow,  or 
green  and  yellow,  are  not  uncommon,  while  in  fewer  cases 
we  find  one  star  white  and  the  other  purple,  or  one  white 
and  the  other  red.  .  In  several  instances  each  star  has  a 
rosy  light. 

The  following  are  a  few  of  the  most  interesting  colored 
double  stars  :  — 


i88 


ASTRONOMY. 


Name  of  star.  Color  of  larger  one. 

y  (gamma)  Andromedae,  Orange, 


Color  of  smaller  one. 

Sea-green. 


a  Piscium, 

£  Cygni, 

77  (eta)  Cassiopeise, 

a-  (sigma)  Cassiopeiae, 

£  (zeta)  Coronse, 

A  star  in  Argo, 

A  star  in  Centaurus, 


Pale  green,  Blue. 

Yellow,  Sapphire-blue. 

Yellow,  Purple. 

Greenish,  Fine  blue. 

White,  Light  purple. 

Pale  rose,  Greenish  blue. 

Scarlet,  Scarlet. 

Single  stars  of  a  fiery  red  or  deep  orange  color  are 
common  enough.  Of  the  first  color  may  be  mentioned 
Aldebaran,  Antares,  and  Betelgeuse.  Arcturus  is  a  good 
example  of  an  orange  star.  Isolated  stars  of  a  deep  blue 
or  green  color  are  very  rarely  found. 

It  is  now  a  well-established  fact  that  the  stars  change 
their  color.  Sirius  was  described  as  a  fiery  red  star  by 
the  ancients.  Some  years  ago  it  was  pure  white,  while  it 
is  now  becoming  of  a  decided  green  color.  Capella  was 
also  called  a  red  star  by  the  ancients ;  it  was  afterwards 
described  as  a  yellow  star ;  and  is  now  bluish.  Many  other 
instances  of  change  of  color,  though  less  decided,  have 
been  detected. 

165.  Variable  Stars.  —  Besides  those  stars  which  are 
known  to  undergo  changes  of  color,  there  are  many  stars, 
not  only  among  those  visible  to  the  naked  eye,  but  also 
belonging  tb  telescopic  classes,  which  exhibit  periodical 
changes  of  brilliancy.  These  are  called  variable  stars. 

Algol,  or  j3  (beta),  in  the  constellation  Perseus,  is  one 
of  the  most  interesting  of  the  variable  stars.  For  about 
2d  i3h  it  shines  as  an  ordinary  star  of  the  second  magni- 
tude, and  is  therefore  conspicuously  visible  to  the  naked 
eye.  In  somewhat  less  than  four  hours  it  diminishes  to 
the  fourth  magnitude,  and  thus  remains  about  twenty 
minutes ;  it  then  as  rapidly  increases  to  the  second,  and 
continues  so  for  another  period  of  2d  i3h,  after  which 


ASTRONOMY.  189 

similar  changes  recur.  The  exact  period  in  which  all 
these  variations  are  performed  is  2d  2oh  48m  55s. 

Another  remarkable  star  of  this  kind  is  o  (omicron)  in 
Cetus,  often  termed  Mira,  or  the  wonderful  star.  It  goes 
through  all  its  changes  in  334  days,  but  exhibits  some 
curious  irregularities.  When  brightest  it  usually  shines 
as  a  star  of  the  second  magnitude,  yet  on  certain  occa- 
sions has  not  appeared  brighter  than  the  fourth.  Between 
five  and  six  months  afterwards  it  disappears  altogether. 
Sometimes  it  will  shine  without  perceptible  change  of 
brightness  for  a  whole  month ;  at  others  there  is  a  very 
sensible  alteration  in  a  few  days.  Its  variability  was  dis- 
covered in  the  seventeenth  century. 

The  list  of  variable  stars  visible  to  the  naked  eye  is 
pretty  numerous.  Among  these  are  the  following  :  — 

8  (delta)  Cephei,  goes  through  its  changes  in  5  d.  9  h. 

77  Aquilae,                          "  "  7*4 

a  Herculis,                        "  "  66  days. 

A  star  in  Aquila,              "  "  72     " 

A  star  in  Corona  Borealis,  "  323     " 

A  star  near  x  (chi)  Cygni,  "  406     " 

30  Hydrae,                        "  «  442     « 

In  some  cases  the  periods  extend  to  many  years.  34 
Cygni,  a  star  whose  fluctuations  were  noticed  as  long  since 
as  1600,  is  supposed  to  complete  its  cycle  of  changes  in 
about  eighteen  years. 

The  bright  star  Capella,  in  the  constellation  Auriga,  is 
believed  to  have  increased  in  lustre  during  the  present 
century,  while  within  the  same  period  one  of  the  seven 
bright  stars  (delta)  in  Ursa  Major,  forming  the  Dipper, 
has  diminished.  Many  instances  of  a  similar  kind  might 
be  mentioned. 

Telescopic  variable  stars  are  very  numerous,  and  have 
lately  excited  much  attention. 


I QO  ASTRONOMY. 

166.  Irregular  or  Temporary  Stars.  —  In  the  present 
state  of  our  knowledge,  it  appears  necessary  to  distin- 
guish between  the  variable  star's,  properly  so  called, 
which  go  through  their  changes  with  some  degree  of 
regularity,  and  are  either  always  visible  or  seen  at  short 
intervals,  and  those  wonderful  objects  that  have  occasion- 
ally burst  forth  in  the  heavens  with  a  brilliancy  in  some 
instances  far  surpassing  the  light  of  stars  of  the  first 
magnitude,  or  even  the  lustre  of  Jupiter  and  Venus,  re- 
maining thus  for  a  short  time,  and  then  gradually  fading 
away.  This  latter  class  are  called  irregular  or  temporary 
stars. 

The  most  celebrated  star  of  this  kind  recorded  in  his- 
tory is  one  which  made  its  appearance  in  1572,  and 
attracted  the  attention  of  Tycho  de  Brahe,  the  Danish 
astronomer,  who  has  left  us  a  particular  description  of 
the  various  changes  it  underwent  while  it  continued  within 
view.  It  was  situated  in  Cassiopeia,  one  of  the  circum- 
polar  constellations,  was  first  seen  early  in  the  autumn 
of  1572,  and  afterwards  dwindled  down,  until  it  became 
so  faint,  in  March,  1574,  that  Tycho  could  no  longer  per- 
ceive it.  During  the  early  part  -of  its  apparition  it  far 
surpassed  Sirius,  and  even  Jupiter,  in  brilliancy,  and 
could  only  be  compared  to  the  planet  Venus  when  she 
is  in  her  most  favorable  position  with  respect  to  the 
earth.  Persons  with  keen  sight  could  see  the  star  at 
noon-day ;  and  at  night  it  was  discernible  through  clouds 
that  obscured  every  other  object.  It  twinkled  more  than 
the  ordinary  fixed  stars  ;  was  first  white,  then  yellow,  and 
finally  very  red. 

Another  temporary  star  became  suddenly  visible  in  Ophi- 
uchus,  in  1604,  and  was  observed  by  Kepler.  Though 
somewhat  inferior  to  Venus,  it  exceeded  Jupiter  and 
Saturn  in  splendor.  Like  Tycho's  star,  it  twinkled  far 
more  than  its  neighbors,  but  was  not  characterized  by 


ASTRONOMY.  19 1 

successive  changes  of  color ;  when  clear  from  the  vapors 
prevalent  about  the  horizon,  it  was  always  white.  This 
object  remained  visible  till  March,  1606,  and  then  disap- 
peared. 

Other  stars,  evidently  of  the  same  class,  are  mentioned 
by  historians  in  remote  times.  One  of  a  less  conspicuous 
character  was  discovered  by  Anthelme,  in  1670,  not  far 
from  ft  Cygni ;  and  another  in  April,  1848,  in  the  constel- 
lation Ophiuchus,  which  rose  to  the  fourth  magnitude, 
and  has  now  faded  away  to  the  twelfth,  so  that  it  cannot 
be  seen  without  a  good  telescope. 

In  May,  1866,  a  remarkable  temporary  star  appeared 
in  the  constellation  of  Corona  Borealis.  At  its  greatest 
brilliancy  it  was  somewhat  above  the  second  magnitude. 
It  rapidly  faded  away  and  early  in  June  was  not  above 
the  ninth  magnitude.  It  may  be  that  these  temporary 
stars  are  merely  variable  stars  of  long  period. 

167.  The  Via  Lactea,  or  Milky  Way.  — The  Via  Lactea, 
Galaxy,  or  Milky  Way,  as  it  is  variously  termed,  is  that 
whitish  luminous  band  of  irregular  form  which  is  seen  on 
a  dark  night  stretching  across  the  heavens  from  one  side 
of  the  horizon  to  the  other. 

To  the  naked  eye  it  presents  merely  a  diffused  milky 
light,  stronger  in  some  parts  than  in  others  ;  but  when 
examined  with  a  powerful  telescope  it  is  found  to  consist 
of  myriads  of  stars,  —  of  millions  upon  millions  of  suns, 
so  crowded  together  that  only  their  united,  light  reaches 
the  unassisted  eye. 

The  general  course  of  the  Milky  Way  is  in  a  great  cir- 
cle, inclined  about  63°  to  the  celestial  equator,  and  inter- 
secting it  in  the  constellations  Cetus  and  Virgo. 

The  distribution  of  the  telescopic  stars  within  its  limits 
is  far  from  uniform.  In  some  regions  several  thousands 
(or  as  many  as  are  seen  by  the  naked  eye  on  a  clear 
night  over  the  whole  firmament)  are  crowded  together 


192  ASTRONOMY. 

within  the  space  of  a  square  degree  :  in  others  a  few  glit- 
tering points  only  are  scattered  on  the  black  ground  of 
the  heavens.  It  presents  in  some- parts  a  bright  glow  of 
light  to  the  naked  eye,  from  the  closeness  of  the  constitu- 
ent stars  ;  in  others  there  are  dark  spaces  with  scarcely 
a  single  star  upon  them.  A  remarkable  instance  of  the 
kind  occurs  in  the  broad  stream  of  the  Via  Lactea,  near 
the  Southern  Cross,  where  its  luminosity  is  very  con- 
siderable ;  but  there  exists  in  the  midst  of  it  a  dark 
oval  or  pear-shaped  vacancy,  distinguished  by  the  early 
navigators  under  the  name  of  the  Coal-Sack.  Similar 
vacancies  occur  in  the  constellations  Scorpio  and  Ophi- 
uchus. 

From  the  results  of  a  numerical  estimate  of  the  stars 
at  various  distances  from  the  circle  of  the  Via  Lactea,  it 
has  been  proved  that  the  stars  are  fewest  in  number  near 
the  poles  of  that  circle,  and  increase  —  slowly  at  first, 
afterwards  more  rapidly  —  until  we  arrive  at  the  Milky 
Way  itself,  where  their  number  is  greatest. 

Hence  it  is  inferred  that  the  stars  which  cover  our 
heavens  are  not  uniformly  distributed  throughout  space, 
but,  as  described  by  Sir  John  Herschel,  "  form  a  stratum, 
of  which  the  thickness  is  small  in  comparison  with  its 
length  and  breadth."  The  solar  system  would  appear  to 
be  placed  somewhat  to  the  northern  side  of  the  middle 
of  its  thickness,  since  the  density  of  the  stars  is  rather 
greater  to  the  south  than  to  the  north  of  the  plane  of  the 
Via  Lactea.  From  these  and  other  considerations,  Sir 
William  Herschel  was  led  to  regard  our  starry  firmament 
as  possessing  in  reality  a  form  of  which  Figure  73  will 
convey  some  idea,  one  portion  being  subdivided  into  two 
branches  slightly  inclined  to  each  other. 

The  earth  being  placed  at  S  (not  far  from  the  point  of 
divergence  of  the  two  streams),  the  stars  in  the  direction 
of  b  and  b  would  appear  comparatively  few  in  number, 


ASTRONOMY. 


but  would  increase  rapidly  as  the  line  of  vision  ap- 
proached e,  e,  or  f,  in  which  directions  we  should  see 
them  most  densely  crowded,  the  rate  of  transition  from 
the  poorer  regions  to  those  richest  in  stars  being  such 
as  we  have  alluded  to  above. 

Near  the  intersection  of  the  streams  e  and  <?,  few  stars 
would  present  themselves,  and  there  would  consequently 
be  a  dark  space,  or  rather  a  space  thinly  covered  with 
stars,  included  within  the  two  branches  of  the  Milky 
Way.  This  exactly  represents  the  actual  appearance 
of  the  heavens  :  the  luminosity  of  the  Milky  Way  does 
separate  into  two  distinct  streams  of  light,  which  remain 
thus  over  an  arc  of  about  150°,  and  then  unite  again. 

1 68.  Clusters  of  Stars  and  Nebula.  —  On  casting  our 
eyes  over  the  heavens  on  a  clear  dark  evening,  we  at 
once  perceive  that  in  some  directions  the  stars  are  clus- 
tered together,  and  in  a  few  instances  so  compressed 
that  the  unaided  eye  cannot  separate  the  members  of 
the  group,  which  assumes  a  hazy,  undefined,  or  cloud- 
like  appearance. 

Among  these  close  assemblages  of  stars  may  be  men- 
tioned the  Pleiades  in  Taurus,  Praesepe  (popularly  termed 
the  Beehive)  in  Cancer,  and  a  remarkable  group  in  the 
9  M 


194  ASTRONOMY. 

sword-handle  of  Perseus,  in  which  the  stars  are  readily 
seen  with  a  common  night-glass,  though  the  whole  has 
a  blurred  aspect  to  the  naked  eye. 

One  of  the  most  magnificent  globular  clusters  in  the 
northern  hemisphere  occurs  in  the  constellation  Hercules, 
between  the  stars  Eta  and  Zeta.  It  is^visible  to  the  naked 
eye  on  dark  nights  as  a  hazy-looking  object ;  and  the  stars 
composing  it  are  readily  seen  with  a  telescope  of  moder- 
ate power.  When  examined  with  a  powerful  instrument, 
its  aspect  is  grand  beyond  conception  :  the  stars,  which 
are  coarsely  scattered  at  the  borders,  come  up  to  a  per- 
fect blaze  in  the  centre.  It  is  shown  in  Figure  74. 

Fig.  74- 


There  is  another  cluster  in  the  constellation  Centaurus, 
of  which  Figure  75  is  a  representation.  To  the  naked  eye 
it  appears  like  a  nebulous  or  hazy  star  of  the  fourth  mag- 
nitude ;  while  in  the  telescope  it  is  found  to  cover  a  space 
two  thirds  of  the  apparent  diameter  of  the  Moon,  over 
which  the  stars  are  congregated  in  countless  numbers. 


ASTRONOMY. 
Fig-  75- 


169.  Nebulous  Stars. — The  nebulce  have  been  already 
described   (75).      In  some    instances,   a  faint   nebulosity, 
usually  of  a  circular   figure   and   several   minutes  in  di- 
ameter, envelopes  a  star  which  is  placed  in  or  very  near 
the  centre.     Such  stars  are  called  nebulous  stars.     There 
is  nothing  in  their  appearance  to  distinguish  them  from 
others   entirely  destitute  of  such   appendages  ;    nor  can 
the    nebulosity  in   which   they  are   situated  be    resolved 
into  stars  with  any  telescopes   hitherto  constructed.     As 
instances  of  nebulous   stars,  may  be  mentioned  one  of 
the   fifth   magnitude,   numbered    55    in    Andromeda,  and 
one  of  the  eighth  magnitude  on  the  borders  of  Perseus 
and  Taurus,  particularly  pointed  out  by  Sir  William  Her- 
schel  as  a  remarkakble  object  of  this  class. 

170.  Variable  Nebula.  —  Nebulae,  as  well  as  stars,  are 
known  sometimes  to  change  in  brilliancy.     A  remarkable 
case  of  this  kind  is  that  of  a  nebula  situated  near  Epsilon 


196  ASTRONOMY. 

Tauri.  At  the  time  of  its  discovery  in  1852  it  was  easily 
seen  with  a  good  telescope,  whereas  in  1861  and  1862  it 
was  invisible  with  instruments  of  far  greater  power,  thus 
proving  that  its  light  must  have  undergone  very  consid- 
erable diminution  in  the  course  of  a  few  years.  A  small 
star  close  to  this  nebula  likewise  faded  within  the  same 
lapse  of  time.  No  probable  cause  has  yet  been  assigned 
for  this  variation  in  the  brightness  of  a  nebula. 

171.  The  Nubeculce,  or  Magellanic  Clouds. —  In  the  south- 
ern hemisphere,  not  far  from  the  pole  of  the  equator,  are 
two  nebulous  clouds  of  unequal  extent,  the  greater  cover- 
ing an  area  about  four  times  that  of  the  lesser  one.  They 
were  termed  Magellanic  clouds,  after  Magellan  the  navi- 
gator, a  name  still  in  very  common  use,  but  on  astronomi- 
cal maps  they  are  usually  called  the  nubecula,  major  and 
minor. 

Both  these  cloud-like  masses  are  distinctly  visible  to  the 
naked  eye  when  the  moon  is  absent ;  the  smaller  one, 
however,  disappears  in  strong  moonlight.  Their  light  is 
white  and  diffused,  resembling  that  of  the  Milky  Way. 
Sir  John  Herschel  examined  these  remarkable  objects 
with  his  powerful  instrument  at  the  Cape  of  Good  Hope, 
and  describes  them  as  consisting  of  swarms  of  stars, 
globular  clusters,  and  nebulae  of  various  kinds,  some  por- 
tions being  quite  irresolvable,  and  presenting  the  same 
milky  appearance  in  the  telescope  that  the  nubeculae  them- 
selves do  to  the  naked  eye. 

It  is  believed  that  the  nubeculae  are  independent  of  the 
Via  Lactea,  since  they  offer  combinations  of  nebulous 
forms  which  rarely  occur  in  that  zone. 


ASTRONOMY.  197 


SUMMARY. 

The  stars  are  not  absolutely  fixed.  Their  twinkling  is 
due  to  atmospheric  conditions,  and  is  caused  by  interference. 

(159.) 

The  number  of  stars  in  the  whole  heavens,  visible  to 
the  naked  eye,  is  about  6,000.  The  telescopic  stars  are  in- 
numerable. ( 1 60. ) 

There  are  about  20  stars  of  the  first  magnitude;  about 
50  or  60  of  the  second ;  and  some  200  of  the  third.  The 
faintest  stars  that  can  be  seen  without  the  aid  of  the  tele- 
scope are  of  the  sixth  magnitude.  (161.) 

The  stars  are  arranged  in  groups  called  constellations. 
Twelve  of  these  are  called  zodiacal  constellations.  (162.) 

Many  of  the  brightest  stars  have  proper  names,  but  stars 
are  usually  designated  by  the  letters  of  the  Greek  alpha- 
bet. ,(163.) 

Many  stars  shine  with  colored  light,  and  in  double  stars 
the  colors  of  the  components  are  often  contrasted.  A  few 
stars  are  known  to  change  their  color.  (164.) 

Stars  often  undergo  changes  of  brightness.  Sometimes 
the  variations  are  periodic,  like  those  of  Algol,  Mira,  and 
some  others.  (165.)  In  other  instances  the  changes  are 
temporary,  as  is  the  case  with  Tycho's  and  Kepler's  stars. 
But  the  changes  of  the  temporary  stars  may  be  periodic, 
recurring  at  very  long  intervals.  This  seems  to  be  the 
case  with  the  temporary  star  of  1866.  (166.) 

The  stars  are  most  numerous  in  the  vicinity  of  the 
circle  of  the  Milky  Way,  and  fewest  in  number  near  the 
poles  of  that  circle.  (167.) 

The  stars  are  also  often  collected  into  clusters,  some  of 
which  are  visible  to  the  unaided  eye,  as  in  the  case  of  the 
Pleiades,  Praesepe,  and  the  faint  cluster  in  the  sword 
handle  of  Perseus  ;  others,  like  the  cluster  in  Hercules, 


198  ASTRONOMY. 

and  that  in  Centaurus,  can  be  made  out  only  with  a  tele- 
scope.    (168.) 

Stars   which    are   enveloped  in  a'  faint   nebulosity   are 
called  nebulous  stars.     (169.) 

The  nebulae  are  sometimes  variable.     (170.) 
Near  the  south  celestial  pole  are  two  nebulous  masses 
called  the  Magellanic  clouds,  or  Nubecula.     (171.) 


III. 

GRAY  IT  Y, 

• 

OR  THE   FORCE  BY  WHICH  THE  HEAVENLY 
BODIES  ACT  UPON  ONE  ANOTHER. 


GRAVITY. 


THE    LAWS   OF  MOTION. 

172.  First  Law  of  Motion.  —  When  a  body  is  put  in  mo- 
tion, it  will  keep  on  moving  in  a  straight  line  with  unvary- 
ing velocity,  unless  some  forces  act  upon  it.  This  fact  is 
called  \hzfirst  law  of  motion.  It  is  impossible  to  establish 
this  fact  by  direct  experiment,  since  we  cannot  put  a  body 
in  motion  where  no  forces  shaH  act  upon  it ;  and  since  we 
cannot  observe  its  motion  through  an  infinite  distance  and 
time.  If  a  wheel  be  made  to  rotate  or  a  pendulum  made 
to  vibrate  in  the  air,  they  soon  come  to  rest.  But  the  fric- 
tion of  the  turning  point,  and  the  resistance  of  the  air,  are 
constantly  offering  hindrance  to  their  motion.  It  is  found 
that  if  the  friction  be  diminished  by  more  delicate  adjust- 
ment of  their  points  of  support,  they  will  keep  in  motion  a 
proportionally  longer  time.  Again,  the  resistance  of  the  air 
can  be  got  rid  of  by  putting  the  wheel  or  pendulum  under 
the  exhausted  receiver  of  an  air-pump.  When  the  resist- 
ance of  the  air  is  thus  removed,  and  the  friction  reduced 
to  the  least  possible  amount,  the  bodies  are  found  to  keep 
up  their  motion  a  very  long  time.  Hence  we  must  con- 
clude that,  if  we  could  get  rid  of  all  external  hindrances, 
the  wheel,  when  once  started,  would  keep  on  rotating  with 
an  unvarying  velocity,  and  also  that  the  pendulum  would 
keep  on  vibrating  at  the  same  rate. 
9* 


202  ASTRONOMY. 

Neither  of  these  is  an  example  of  motion  in  a  straight 
line,  but  from  these  circular  motions  we  conclude  that  a 
body  when  once  put  in  motion,  and'  not  acted  upon  by  any 
force,  would  move  in  a  straight  line  with  a  uniform  velocity. 
For  mathematical  investigation  has  shown  that  if  the  parts 
of  a  body  when  unconstrained  would  move  in  a  straight 
line  with  uniform  velocity,  then,  when  they  are  so  con- 
strained by  their  connection  with  one  another  that  they  are 
obliged  to  move  in  circles,  the  body  will  rotate  with  a  uni- 
form velocity;  and  that  if  the  parts  of  a  body,  when  uncon- 
strained, would  not  move  in  straight  lines  with  an  unvary- 
ing velocity,  then  they  would  not  rotate  with  a  uniform 
velocity.  Mathematical  investigation  has  also  shown  that 
the  only  way  to  account  for  the  uniform  vibration  of  a  free 
pendulum  is  to  suppose  that  the  pendulum-ball  would 
move  in  a  straight  line  with  a  uniform  rate,  if  left  to  itself 
after  it  has  been  once  started. 

173.  The  Planets   and  Satellites   are  acted  on   by  some 
Force. — We  have  seen  that  all  the  planets  and  satellites 
move  in  curved  lines  ;   hence  they  must  be  acted  on  by 
some  force,  and  this  force  must  be  constant  in  its  action, 
since  they  move  in  straight  lines  in  no  part  of  their  orbits. 

174.  Second  Law  of  Motion.  —  It  is  well   known   that 
when  a  body  is  held  in  the  hand  it  presses  upon  it,  and 
when  it  is  left  unsupported  it  falls  to  the  ground.     This 
shows  that  there  is  a  force  acting  between  the  earth  and 
the  body,  which  draws  the  two  together.     It  is  this  force 
which  gives  bodies  weight ;   that  is,  which  causes  them  to 
exert  pressure.     It  is  therefore  called  gravity. 

The  second  law  of  motion  is,  that  when  a  moving  body 
is  acted  upon  by  gravity  alone,  it  will,  at  a  given  time,  be 
just  as  far  from  the  point  which  it  would  have  reached  had 
it  been  left  to  itself,  as  it  would  have  been  had  it  been  at 
rest  at  that  point  in  the  first  place,  and  been  acted  upon  by 
gravity  alone  during  the  same  time. 


ASTRONOMY. 


203 


Suppose  that  a  body,  for  instance,  is  moving  in  the  di- 
rection of  A  B  (Figure  77)  with  a  velocity  which  would 
carry  it  from  A  to  B  in  one  sec- 
ond of  time,  and  suppose  that 
the  force  of  gravity  would  draw 
it  in  the  same  time  from  a  posi- 
tion of  rest  at  A  to  C;  then  at 
the  end  of  the  second  the  body 
will  be  found  at  D,  having  been 
pulled  away  from  the  place  B, 
which  it  would  have  reached 
with  the  original  direction  and 

velocity,  just  as  much  as  if  pulled  away  from  the  state 
of  rest.     That  is,  BD  just  equals  AC. 

This  law  may  be  illustrated  by  experiments  in  the  follow- 
ing manner:    AB  (Figure  78)  is  a  board;   CD  an  arm 

Fig.  78. 


moving  upon  it,  turning  on  a  hinge  at  C,  and  driven  by  a 
spring  E ;  at  the  end  D  of  the  arm  is  a  hollow,  with  its 
opening  in  the  side  of  the  arm  large  enough  to  contain  a 
small  ball,  so  that  when  the  arm  is  driven  by  the  spring 
£,  the  ball  will  be  thrown  horizontally  from  the  hollow 
at  D ;  at  F  is  another  chamber  opening  downwards,  its 
lower  opening  being  stopped  by  a  board  G,  which  will  be 


204  ASTRONOMY. 

knocked  away  by  a  blow  of  the  arm  CD ;  then  it  is  plain 
that  if  one  ball  be  put  in  D  and  another  in  JE,  the  very  same 
movement  which  throws  one  ball  forward  causes  the  other 
ball  to  drop  at  the  same  instant ;  and,  if  the  second  law  of 
motion  be  true,  one  of  them  will  fall  down  vertically  to  the 
floor  at  H  at  the  sanje  instant  at  which  the  other,  which  is 
projected  forward,  reaches  the  floor  at  K.  And  the  two 
balls  do  reach  the  floor  at  the  same  instant ;  proving  that 
if  a  ball  is  thrown  horizontally,  it  falls  from  that  horizontal 
line  down  to  the  ground  in  the  same  time  as  a  ball  which 
dropped  from  a  state  of  rest. 

This  experiment  is  equally  applicable  to  an  inclined 
throw,  if  the  floor  upon  which  the  balls  fall  be  inclined 
exactly  in  the  same  degree. 

175.  AtwoocTs  Machine.  — The  same  is  found  to  be  true 
whatever  be  the  direction  in  which  the  ball  is  projected ; 
though  the  apparatus  used  in  the  above  illustration  is  not 
suited  to  show  this  when  the  ball  is  thrown  either  verti- 
cally upward  or  downward.  The  case  in  which  the  body 
is  projected  vertically  downward  can  be  best  illustrated  by 
an  instrument  called  Atwood's  machine,  shown  in  Figure 
79.  It  consists  of  an  upright  column,  with  a  pulley  at 
the  top  arranged  to  run  with  the  least  possible  friction. 
Over  this  pulley  passes  a  cord,  to  which  are  attached  the 
equal  weights  B  and  E.  C  and  F  are  movable  shelves, 
the  former  of  which  has  a  circular  hole  in  the  centre 
large  enough  to  let  the  weight  B  pass  through  it.  A  is 
a  clock  beating  seconds,  and  carried  by  the  pendulum  D. 
When  we  wish  to  make  the  weight  B  fall,  we  place  upon 
it  a  small  horizontal  bar  of  iron,  which  is  too  long  to 
pass  through  the  hole  in  the  shelf  C.  When,  therefore, 
the  weight  drops  through  this  hole,  the  bar  will  be  caught 
off  and  will  remain  upon  the  shelf. 

If  the  weight  B  with  the  bar  upon  it  be  allowed  to  fall, 
it  will  be  found  that  the  force  of  gravity  will  pull  it  down 


ASTRONOMY. 


205 


one   inch   during   one    second.  Fi&  79- 

Now  adjust  the  shelf  C  so  that 
the  bar  shall  be  removed  at  the 
end  of  the  first  second  ;  it  will 
then  be  found  that  the  weight 
will  fall  two  inches  the  next  sec- 
ond. At  the  end  of  the  first 
second,  then,  the  weight  is  pro- 
jected vertically  downward  with 
a  velocity  of  two  inches  a  sec- 
ond. If  now  the  bar  is  left  on 
during  both  seconds,  the  weight 
will  be  found  to  have  fallen 
three  inches  during  the  second 
second.  Hence  the  force  of 
gravity  pulls  the  weight  down 
the  second  second  an  inch  far- 
ther than  its  velocity  at  the  be- 
ginning of  this  second  would 
have  carried  it ;  that  is,  just  as 
far  as  gravity  would  have  pulled 
it  from  a  state  of  rest. 

By  means  of  this  same  ma- 
chine the  case  of  a  body  pro- 
jected vertically  upward  can  be 
illustrated.  While  one  of  the 
weights  is  falling  the  other 
weight  is  rising.  Suppose  that 
one  bar  be  placed  upon  the  as- 
cending weight,  and  two  on  the 
descending  weight ;  the  second 
a  little  heavier  than  the  first,  so 
that  it  shall  bear  the  same  ratio 
to  the  whole  weight  now  as  the  one  bar  used  at  first.  We 
have  already  seen  that  this  bar,  acting  during  one  second, 


206  ASTRONOMY. 

will  give  one  of  the  weights  a  velocity  downward  of  two 
inches  a  second,  and  the  other  weight  the  same  velocity 
upward.  Suppose  now  that  at  the"  end  of  the  first  second 
both  bars  be  caught  off  the  descending  weight,  the  other 
weight  will  rise  not  two  inches  but  only  one  during  the  next 
second.  Had  it  not  been  for  the  action  of  gravity  upon 
the  bar  resting  on  it,  it  would  have  risen  two  inches.  But 
we  have  already  seen  that  gravity  acting  upon  this  bar 
will  cause  the  weight  to  fall  one  inch  from  a  state  of  rest ; 
hence  it  is  pulled  just  as  far  from  the  place  it  would  have 
reached  as  it  would  have  been  pulled  from  a  state  of 
rest. 

This  action  of  gravity  upon  a  moving  body  causes  it  to 
move  in  a  curve  in  every  case  except  when  the  body  is 
moving  vertically  upward  or  downward.  In  the  first  of 
these  cases  it  merely  retards  the  motion  of  the  body  at  a 
uniform  rate,  and  in  the  second  case  it  accelerates  it  in 
the  same  manner. 

176.  Curvilinear  Motion.  —  The  form  of  the  curve  de- 
scribed by  a  moving  ball  depends  upon  the  velocity  with 

which  it  is  moving  and 

r  ig.  80. 

the  strength  of  the 
force  of  gravity.  The 
velocity  of  the  body 
being  the  same,  the 
greater  the  force  of 
gravity,  the  more  rap- 
idly does  the  path  described  by  the  body  curve.  This  is 
shown  in  Figure  80.  If  the  ball  is  moving  with  a  velocity 
which  would  carry  it  from  A  to  B  in  a  second,  and  the 
force  of  gravity  would  carry  it  from  a  state  of  rest  at  A  to 
C  in  the  same  time,  then  A  D  will  be  the  curvature  of  its 
path,  BD  being  equal  to  A  C.  If  gravity  could  carry 
it  from  A  to  O  in  a  second,  then  A  D'  would  represent 
the  curvature  of  its  path,  B  D'  being  equal  to  A  C. 


ASTRONOMY.  207 

A  D'  obviously  curves  more  rapidly  than  A  D.  Again, 
the  force  of  gravity  being  the  same,  the  less  the  ve- 
locity with  which  the  ball 

'  Fig.  81. 

is  moving,  the  more  rap- 
idly does  its  path  curve. 
Thus,  in  Figure  81,  if  the 
force  of  gravity  would  car- 
ry the  body  from  a  state 
of  rest  at  A  to  C  in  a  second,  and  the  velocity  of  the 
body  be  such  that  it  would  move  from  A  to  B  in  the 
same  time,  then  A  D  will  represent  its  path.  But  if  its 
velocity  would  carry  it  from  A  to  B'  in  a  second,  then  A  D' 
would  represent  its  path.  But  A  D  obviously  curves  more 
rapidly  than  A  D'.  Everybody  knows  that  when  a  stone 
is  thrown  from  the  hand,  its  path  is  much  curved,  and  it 
reaches  the  ground  before  it  has  gone  far.  But  if  you 
watch  the  motion  of  a  cannon  ball,  which  you  may  do  if 
you  stand  behind  a  cannon  when  it  is  fired,  as  you  can  then 
see  the  ball  from  the  time  it  leaves  the  cannon's  mouth  to 
a  distance  of  half  a  mile  or  more,  you  will  perceive  that 
its  path  is  curved,  but  very  much  less  curved  than  the  path 
of  the  stone  :  in  fact  it  is  nearly  straight.  The  ball  drops 
downward  through  the  same  space  as  the  stone  in  one  sec- 
ond of  time,  but  it  moves  much  farther  in  a  horizontal  di- 
rection in  the  same  time. 

177.  The  Force  which  curves  the  Paths  of  the  Planets  is 
always  directed  towards  the  Sim.  —  Since  the  planets  are 
carried  along  with  the  sun  in  his  journey  among  the  stars, 
it  would  seem  that  there  must  be  some  force  which  holds 
them  together.  Is  this  the  same  force  as  that  which 
curves  their  orbit,  and  as  that  which  draws  a  stone  to 
the  earth  ?  Since  the  path  of  a  planet  curves  round  in 
the  same  direction  throughout  its  whole  extent,  the  force 
which  curves  this  path  must  be  constantly  pulling  the 
planet  towards  some  point  inside  its  orbit. 


208 


ASTRONOMY. 


Fig.  82. 


Long  before  the  theory  of  gravitation  was  established 
by  Newton,  Kepler  had  discovered  that  if  a  line  be  drawn 
from  the  sun  to  a  planet,  this  line  sweeps  over  equal  areas 
in  equal  times  in  every  part  of  the  planet's  orbit. 

In  Figure  82,  suppose  »S  to  be  the  position  of  the  sun, 
and  the  curved  line  to  be  the  orbit  of  the  planet.  Sup- 
pose the  planet  to  be  at  a,  moving  in  the  direction  a  b 

with  a  velocity  which  would 
carry  it  to  b  in  a  unit  of 
time,  and  that  a  force  pull- 
ing it  toward  the  sun  acts 
upon  it  for  only  an  instant, 
giving  it  a  velocity  which 
would  carry  it  to  g  in  the 
same  time.  Draw  the  line 
b  c  parallel  to  a  g  and  take 
b  c  equal  to  ag;  the  point 
c  will  be  the  position  of  the 
body  at  the  end  of  the  unit 
of  time,  and  the  straight 

line  a  c  will  be  the  path  passed  over  by  the  body.  If  the 
body  were  left  to  itself  the  next  unit  of  time,  it  would 
pass  on  in  a  straight  line  to  //,  a  distance  equal  to  a  c. 
Suppose  now  it  be  acted  upon  by  another  instantaneous 
impulse  drawing  it  towards  the  sun,  and  sufficient  to  carry 
it  from  a  state  of  rest  at  c  to  /  in  the  same  time  ;  its 
position  at  the  end  of  the  time  will  be  at  ^,  found  by 
drawing  d  e  equal  and  parallel  to  c  f,  and  its  path  will 
be  the  straight  line  c  e.  Since  d  e  is  parallel  to  c  fy  the 
two  triangles  See  and  S  c  d  have  the  same  base  and  equal 
altitudes,  and  are  consequently  equal. 

But  a  c  and  cd  are  also  equal,  and  the  two  triangles  a  S  c 
and  c  S  d  have  equal  bases  and  the  same  altitude,  since 
their  vertices  are  at  the  same  point ;  hence  these  triangles 
are  equal,  and  therefore  S  a  c  is  equal  to  S  c  e.  So  long 


ASTRONOMY.  209 

then  as  the  planet  is  subjected  to  a  succession  of  instanta- 
neous impulses  at  equal  intervals  which  draw  it  towards 
the  sun,  the  areas  passed  over  by  an  imaginary  line  joining 
the  planet  and  the  sun  during  each  of  these  intervals  will 
be  equal.  This  will  be  true  whatever  be  the  duration  of 
the  intervals  and  the  strength  of  the  instantaneous  im- 
pulses, whether  these  impulses  are  equal  or  not.  It  will 
therefore  be  true  when  the  interval  between  the  succes- 
sive impulses,  equal  or  not,  is  infinitely  small ;  that  is, 
when  the  force  drawing  the  planet  toward  the  sun  acts 
continuously.  In  this  case  the  path  becomes  a  curve, 
that  is,  a  line  bent  at  every  point  Not  only  are  these  tri- 
angles equal  when  the  impulses  are  directed  toward  the  sun, 
but  they  will  not  be  equal  when  the  impulses  are  directed 
toward  any  other  point.  The  force,  then,  that  curves  the 
paths  of  the  planets  must  be  directed  toward  the  sun.  The 
same  is  true  of  the  moon's  path  and  the  earth. 

178.  The  Force   that  deflects   the  Moon's    Path    is   the 
same  as  that  which  draws  a  Stone  to  the  Earth.  —  Having 
thus  determined  from  Kepler's  second  law  that  the  force 
which  deflects  the  moon's  path  is  directed  towards  the 
earth,  Newton  inquired  whether  this  force  was  the  same 
as  that  which  drew  a  stone  to  the  earth,  on  the  supposi- 
tion that  this  force,  like  light,  diminishes  in  intensity  as 
the  square  of  the  distance   increases  ;  that  is,  becomes 
four    and    nine   times   less   when   the   distance    becomes 
twice  or  thrice  as  great. 

In  order  to  understand  how  Newton  pursued  this  in- 
quiry, we  must  see  how  gravity  causes  bodies  to  fall  at 
the  surface  of  the  earth. 

179.  Gravity  would  cause  all  Bodies  to  fall  at* the  same 
Rate,  were  it  not  for  the  Resistance  offered  by   the  Air. 
—  As  we  observe  bodies  light  and  heavy  falling  through 
the  air,  we  come  to  think  that  the  force  of  gravity  causes 
heavy  bodies  to  fall  more  rapidly  than  light  ones ;  but  if 

N 


210 


ASTRONOMY. 


Fig.  83. 


we  place  a  coin  and  a  feather  in  a  long  glass  tube  and  ex- 
haust the  air  completely,  on  inverting  the   tube  (Figure 
83)  the  two  bodies  will  fall  through  it  in  the  same  time. 
It  is  therefore  the  resistance  of  the  air 
which  causes  a  light  body  to  fall  more 
slowly  through  the  atmosphere  than  a 
heavy  one  does. 

When  therefore  the  force  of  gravity 
is  unimpeded  in  its  action,  it  will  cause 
every  body,  whatever  may  be  its  size, 
shape,  or  density,  to  fall  with  exactly 
the  same  speed.  We  next  inquire  how 
far  gravity  will  cause  a  body  to  fall  in  a 
second  of  time.  This  is  determined 
by  means  of  the  pendulum. 

THE  PENDULUM. 

1 80.  A   pendulum  is  a  heavy  body 
suspended  from  a  fixed  point  by  means 
of  a  cord  or  rod.     When  the  centre  of 
gravity  of  the  body  is  directly  under 
the  point  of  support,  the  body  remains 
at  rest ;  but  if  the  body  be  drawn  out 
of  this  position,   it  will,  on  being   re- 
leased, fall  towards  a  vertical  line  pass- 
ing through  the  point  of  support,  and 
when  it  has  reached  this  line  it  will, 
owing  to  its  inertia,  pass  beyond  it.     On  coming  to  rest,  it 
again  falls  toward  this  vertical  line  and  again  passes  be- 
yond, and  thus  continues  to  oscillate  from  side  to  side. 

In  studying  the  movements  of  the  pendulum,  mathema- 
ticians have  considered  two  kinds  of  pendulum,  which  they 
have  called  the  simple  pendulum  and  the  compound  pen- 
dulum. 


ASTRONOMY. 


211 


Fig.  84. 


1 


1 8 1.  The  Simple  Pendulum. — A  simple  pendulum  con- 
sists of  a  material  point,  suspended  to  a  fixed  point  by 
means  of  a  thread  without  weight,  perfectly  flexible,  and 
incapable  of  stretching.  Such  a  pendulum  has  of  course 
no  real  existence ;  but  we  can  approach 
sufficiently  near  to  it,  for  purposes  of  il- 
lustration, by  suspending  a  small  lead 
bullet  to  a  fixed  point  by  means  of  a 
fine  silk  thread. 

182.  First  Law  of  the  Oscillation  of  the 
Pendulum.  —  Suppose  d,  in  Figure  84, 
to  be  a  leaden  ball  hanging  by  a  fine 
silk  thread.  Pull  it  to  one  side  so  that  it 
shall  vibrate  through  an  arc  of  some  3°, 
and  count  the  number  of  its  oscillations 
in  a  minute.  Now  bring  it  to  rest  again, 
and  draw  it  to  one  side  so  that  it  shall 
oscillate  through  an  arc  of  2°,  and  again 
count  its  oscillations  in  a  minute.  Again 
bring  the  ball  to  rest,  then  cause  it  to 
oscillate  through  an  arc  of  i°,  and  count 
the  oscillations  in  a  minute.  In  all  three  cases  the  num- 
ber of  oscillations  in  a  minute  will  be  equal. 

By  an  oscillation  is  meant  the  whole  of  the  pendulum's 
movement  in  one  direction.  The  arc  through  which  the 
pendulum  oscillates  is  called  the  amplitude  of  its  oscilla- 
tion. 

The  above  experiment  shows  that  when  the  length  of  the 
pendulum  remains  the  same,  and  the  amplitude  of  the  oscilla- 
tion does  not  exceed  3°,  the  pendulum  always  oscillates  in  the 
same  time,  whatever  be  the  amplitude  of  the  oscillation. 

This  singular  property  of  the  pendulum  is  called  its 
isochronism,  from  two  Greek  words  signifying  equal  times, 
and  the  oscillations  of  the  pendulum  are  said  to  be  isoch- 
ronous. 


212  ASTRONOMY. 

183.  Second  Law  of  the  Oscillation  of  the  Pendulum.  — 
Let  d  and  r,  in  figure  84,  be  two  pendulums  exactly  alike, 
except  that  the  ball  of  one  is  lead  •  and  of  the  other  ivory. 
Let   each    oscillate    through  a  small   arc,   and   count   its 
oscillations  in  a  minute.     It  will  be  found  that,  making 
allowance  for  the  resistance  of  the  air,  each  performs  the 
same  number  of  oscillations  in  the  same  time.     This  gives 
the  second  law  of  the  oscillation  of  the  pendulum,  namely : 

for  pendulums  of  the  same  length  the  duration  of  the  oscilla- 
tion is  the  same,  whatever  be  the  substance  of  which  the  pen- 
dulum is  formed. 

184.  Third  Law  of  the  Oscillation  of  the  Pendulum.  — 
Let  b,  in  Figure  84,  be  a  pendulum  one  fourth  the  length 
of  <r,  and  a  another,  one  ninth  the  length  of  c.     Set  each 
oscillating  through  a  small  arc,  and  count  the  oscillations 
of  each  in  a  minute.     It  will  be  found  that  b  oscillates 
twice  as  fast  as  ct  and  a  thr.ee  times  as  fast  as  c.     This 
shows  that,  for  pendulums  of  unequal  length,  the  duration  of 
the  oscillation  is  proportional  to  the  square  root  of  the  length  ; 
that  is,  the  lengths  of  the  pendulum  being  made  4,  9,  and 
1 6  times  greater,  the  duration  of  the   oscillation  of  the 
pendulum  will  be  only  2,  3,  and  4  times  longer.     This  is 
the  third  law  of  the  oscillation  of  the  pendulum. 

185.  Fourth  Law  of  the  Oscillation  of  the  Pendulum. — 
It  is   found  that  when  a  pendulum  of  a  given  length  is 
placed  on  different  parts  of  the  earth's  surface,  the  dura- 
tion of  the  oscillations  is  not  always  the  same.     Towards 
the  poles  it  is  found  to  oscillate  more  rapidly  than  at  the 
equator.     Mathematicians  have  shown  that  this  is  because 
the  force  of  gravity  is  stronger  at  the  poles.     They  have 
shown  that,  in  different  parts  of  the  earth  the  duration  of  the 
oscillations  for  pendulums  of  the  same  length  is  in  the  inverse 
ratio  of  the  square  root  of  the  intensity  of  gravity ;  that  is, 
if  the  intensity  of  gravity  were  four  times  as  great  in  one 
place  as  in  another,  the  duration  of  the  oscillations  of  a 


ASTRONOMY.  213 

pendulum  of  the  same  length  would  be  half  as  great,  and 
so  on. 

1 86.  The  Formula  of  the  Pendulum.  —  Let  /  represent 
the  duration  of  an  oscillation ;  /,  the  length  of  the  pendu- 
lum ;  g,  the  intensity  of  gravity,  that  is,  the  velocity  ac- 
quired at  the  end  of  a  second  by  a  body  which  falls  in  a 
vacuum  ;  and  *-  =  3.i4i6  :  and  mathematicians  have  found 
that  the  above  laws  can  be  summed  up  in  the  following 
expression  :  — 


g 

This  expression  is  called  the  formula  of  the  pendulum. 

187.  The  Compound  Pe?idulum.  —  The  simple  pendulum, 
as  has  been  stated,  can  have  no  real  existence.  Every 
pendulum  actually  used  is  a  compound  pendulum,  consist- 
ing of  a  heavy  weight  suspended  from  a  fixed  point  by 
means  of  a  rod  of  wood  or  metal.  The  particles  of  such 
a  pendulum  must  of  course  be  at  different  distances  from 
the  point  of  suspension,  and  must  therefore  tend  to  oscil- 
late in  different  times.  Hence  the  time  of  oscillation  of 
the  whole  pendulum  will  npt  be  the  same  a£  that  of  a  sim- 
ple pendulum  of  the  same  length. 

The  compound  pendulum  may  be  regarded  as  consisting 
of  as  many  simple  pendulums  as  it  contains  particles.  If 
these  were  free  to  move,  they  would  oscillate  in  times  de- 
pending upon  their  distances  from  the  point  of  suspension ; 
but  since  they  are  united  in  one  body,  they  are  all  com- 
pelled to  oscillate  in  'the  same  time.  Consequently,  the 
oscillations  of  the  particles  near  the  point  of  suspension 
are  retarded  by  the  slower  oscillations  of  the  particles  be- 
low them ;  and,  on  the  other  hand,  the  oscillations  of  the 
particles  near  the  lower  end  of  the  pendulum  are  acceler- 
ated by  the  more  rapid  oscillations  of  those  above  them. 
At  some  point  between  these  there  must  be  a  particle 
whose  oscillation  is  neither  retarded  nor  accelerated,  —  all 


214  ASTRONOMY. 

the  particles  above  having  just  the  same  tendency  to  oscil- 
late faster  that  those  below  have  to  oscillate  slower.  This 
point  is  called  the  centre  of  oscillation,  and  it  is  obvious 
that  the  time  of  oscillation  of  a  compound  pendulum  is 
the  same  as  that  of  a  simple  pendulum  whose  length  is 
equal  to  the  distance  of  the  centre  of  oscillation  from  the 
point  of  suspension.  This  distance  is  the  virtual  length 
of  the  pendulum,  and  the  formula  given  above  (186)  will 
apply  to  compound  pendulums  by  making  /=  their  virtual 
length.  By  the  length  of  a  pendulum,  whatever  may  be  its 
form,  we  are  always  to  understand  the  virtual  length,  unless 
the  reverse  is  expressly  stated. 

When  the  form  of  the  pendulum  is  given,  the  position 
of  the  centre  of  oscillation  can  be  calculated  by  methods 
belonging  to  the  higher  mathematics.  It  can  also  be 
found  experimentally  by  making  use  of  a  remarkable  prop- 
erty of  the  compound  pendulum,  by  virtue  of  which,  if 
such  a  pendulum  be  inverted  and  suspended  by  its  centre 
of  oscillation,  its  former  point  of  suspension  will  become 
its  new  centre  of  oscillation,  and  the  time  of  vibration  will 
be  the  same  as  before ;  or,  as  it  is  usually  expressed,  the 
centres  of  oscillation  and  suspension  are  interchangeable. 

To  find  the  centre  of  oscillation,  then,  we  have  only  to 
reverse  a  pendulum,  and  by  trial  find  the  point  at  which  it 
must  be  suspended  in  order  to  oscillate  in  the  same  time 
as  it  did  before  it  was  reversed.  A  pendulum  constructed 
for  this  purpose  is  called  a  reversible  pendulum. 

1 8 8.  The  Use  of  the  Pendulum  for  measuring  the  Force  of 
Gravity.  —  By  transposing,  we  get  from  the  equation  above 

(185)  g  =•  I  —2;  from  which,  when  we  know  the  length 

of  a  pendulum  which  oscillates  in  a  given  time,  T,  we  can 
easily  calculate  the  value  of  g  for  the  place  of  experiment. 
If,  in  the  last  equation,  we  make  T=  i,  then  /denotes  the 
length  of  a  pendulum  beating  seconds,  and  we  find  that 


ASTRONOMY.  215 

g  =  1 7T2.  In  order,  then,  to  measure  the  intensity  of 
gravity  at  any  place,  we  have  only  to  oscillate  a  pendulum 
whose  virtual  length  is  known,  and  observe  the  length  of 
a  single  oscillation.  This  is  readily  done  by  counting  a 
large  number  of  oscillations,  and  observing  the  time  occu- 
pied by  the  whole  number.  This  time,  divided  by  the 
number  of  oscillations,  gives  the  time  of  a  single  oscilla- 
tion very  accurately,  because  any  error  which  may  have 
been  made  in  observing  the  time  is  thus  greatly  divided. 

Now  it  has  been  found  that  a  pendulum  beating  seconds 
at  London  must  be  39.13929  inches  in  length.  Substitut- 
ing this  value,  and  also  that  of  ir2  in  the  equation,  g  =  I  ^r2, 
we  get  g  =  386  inches. 

Since  the  velocity  of  a  ball  is  zero  at  starting,  and  at  the 
end  of  a  second  it  attains  the  velocity  of  386  inches,  its 
mean  velocity  would  be  193  inches,  and  this  is  evidently 
the  distance  the  body  would  be  drawn  towards  the  earth  by 
gravity  in  a  second  of  time. 

We  have  thus  found  the  answer  to  the  question  asked  in 
section  179,  and  have  proved  that  gravity  causes  a  body  to 
fall  sixteen  feet  in  a  second  of  time. 

SUMMARY   OF   THE   PENDULUM. 

A  pendulum  is  a  heavy  body  suspended  from  a  fixed 
point  by  means  of  a  cord  or  rod.  (180.) 

The  laws  of  the  oscillation  of  the  pendulum  are  best 
investigated  by  means  of  a  simple  pendulum.  (181.) 

These  laws  are  four  in  number. 

i  st.  When  the  length  of  the  pendulum  remains  the  same, 
and  the  amplitude  of  the  oscillations  does  not  exceed  3°,  the 
pendulum  always  oscillates  in  the  same  time.  (182.) 

2d.  For  pendulums  of  the  same  length,  the  duration  of  the 
oscillations  is  the  same,  whatever  be  the  substance  of  which 
the  pendulum  is  formed.  (183.) 


2l6  ASTRO  XO  MY. 

3d.  For  pendulums  of  different  lengths,  at  the  same  placey 
the  duration  of  the  oscillation  is  proportional  to  the  square 
root  of  the  lengths.  (184.) 

4th.  ///  different  parts  of  the  earth  the  duration  of  the  os- 
cillation for  pendulums  of  the  same  length  is  in  the  inverse 
ratio  of  the  square  root  of  the  intensity  of  gravity.  (185.) 

These  laws  can  be  summed  up  in  the  following  expres- 
sion, called  the  formula  of  the  pendulum :  — 


The  pendulum  in  actual  use  is  a  compound  pendu- 
lum. (187.) 

The  pendulum  is  used  for  measuring  the  force  of  grav- 
ity. (188.) 

GRAVITY   ACTS    BETWEEN    THE    EARTH   AND 
THE   MOON. 

189.  The  Intensity  of  Gravity  varies  directly  as  the  Mass 
of  the  Body  acted  upon  by  this  Force.  —  It  has  been  shown, 
by  the  falling  of  bodies  in  a  vacuum  (179),  and  the  pen- 
dulum (188),  that  gravity  acting  upon  a  body  at  rest  will 
cause  it  to  fall  one  hundred  and  ninety-three  inches  in  a 
second,  whatever  may  be  the  amount  of  matter  that  the 
body   contains.      But   if    one    body   contains    twice    the 
amount  of  matter  that  another  does,  it  will  clearly  take 
twice   the   force   to   pull   it   through   the   same   distance. 
Hence  the  intensity  of  gravity  acting  upon  bodies  near 
the  earth  must  vary  directly  as  the  amount  of  matter  which 
they  contain,  or  as  the  mass  of  the  bodies. 

190.  The  Moon's  Path  is  curved  by  the  Force  of  Grav- 
ity.—  We  now  return  to  the  consideration  of  the  Moon's 
path,  and  the  force  which  deflects  it.     (178). 

We  have  found  that  gravity  acts  between  the  earth  and 


ASTRONOMY.  2  I  7 

a  body  near  its  surface  with  a  force  whose  intensity  varies 
directly  as  the  mass  of  the  body,  and  is  sufficient  to  draw 
it  from  a  state  of  rest  193  inches  in  a.  second. 

If,  then,  the  earth's  attraction  at  the  distance  of  3,959 
miles  from  its  centre  draws  a  body  193  inches  in  a  second, 
how  far  in  a  second  ought  it  to  draw  a  body  distant 
238,800  miles  from  this  centre,  supposing  that  the  force 
diminishes  in  proportion  as  the  square  of  the  distance 
increases  ?  This  distance  will,  of  course,  diminish  with 
the  intensity  of  gravity,  and  can  easily  be  ascertained  by 
squaring  these  two  numbers,  rinding  how  many  times  the 
less  of  these  squares  is  contained  in  the  greater,  and  di- 
viding 193  inches  by  the  quotient.  This  distance  is  thus 
found  to  be  .05305  of  an  inch.  We  must  Fig  8s> 

now  find   how  much  the   moon's   path  is  -m,     M 

really  deflected  in  one  second  of  time. 
Let  J5,  in  Figure  85,  represent  the  position 
of  the  earth ;  M,  the  position  of  the  moon ; 
and  Mm,  the  direction  in  which  the  moon 
is  moving  at  the  instant.  Let  Mm  be  the 
distance  the  moon  would  pass  over  in  one  second  of  time 
if  nothing  interfered  with  her  motion.  Then  m  JVwill  be 
the  distance  the  moon  is  drawn  towards  the  earth  in  this 
time.  Now,  considering  the  moon  as  moving  in  a  cir- 
cle whose  semidiameter  is  her  mean  distance,  E  M  is 
238,800 ;  .the  whole  circumference  is  1,500,450  miles ;  and 
her  periodic  time  is  27  days,  7  hours,  43  minutes.  Dividing 
the  length  of  the  whole  orbit  by  the  number  of  seconds  in 
her  periodic  time,  we  find  her  velocity  in  any  part  of  her 
orbit,  as  at  M,  is  .6356  of  a  mile.  This  is  the  distance, 
Mm,  that  she  would  have  travelled,  had  no  force  inter- 
fered with  her  motion.  But  E  M  m  is  a  right-angled  trian- 
gle, and  we  know  the  length  of  the  sides  E  Mand  Mm. 
By  squaring  these  and  extracting  the  square  root  of  their 
sum,  we  find  the  length  of  the  hypothenuse  E  m  to  be 


2l8  ASTRONOMY. 

238,800.0000008459  miles.  But  m  TV  is  equal  to  m  E  mi- 
nus E  N.  Therefore  m  N  is  equal  to  .0000008459  of  a 
mile,  or  .0536  of  an'  inch.  This  is  found  to  be  almost  ex- 
actly the  same  distance  that  the  moon  ought  to  be  drawn 
to  the  earth  in  a  second  of  time,  provided  she  is  drawn 
downward  by  the  same  force  which  draws  a  stone  to  the 
earth,  the  intensity  of  the  force  having  diminished  as  the 
square  of  the  distance  has  increased.  This  slight  differ- 
ence is  exactly  accounted  for  by  disturbing  causes  which 
are  known  to  exist.  It  is  therefore  certain  that  the  attrac- 
tion of  the  earth  which  causes  the  stone  to  fall,  and  the 
attraction  of  the  earth  which  bends  the  moon's  path  from 
a  straight  line  to  a  circle,  are  really  the  same  attraction, 
only  diminished  for  the  moon  in  the  inverse  proportion 
of  the  square  of  her  distance. 

If  we  had  taken  the  interval  of  an  hour  instead  of  a 
second,  we  should  have  found  that  the  moon  was  drawn  to 
the  earth  10.963  miles ;  and  we  should  have  found  that 
a  stone  at  the  distance  of  the  moon  would  have  fallen 
through  a  corresponding  space  in  the  same  time. 

GRAVITY   ACTS   BETWEEN  THE   SUN   AND 

PLANETS,  AND  BETWEEN  PLANETS 

AND  THEIR  MOONS. 

191.  The  Paths  of  the  Earth  and  of  Jupiter  are  curved 
by  the  Force  of  Gravity.  —  We  will  proceed  to  see  whether 
the  paths  of  the  planets  are  curved  by  gravity. 

Let  us  first  compare  the  spaces  through  which  the  sun 
draws  the  planets  in  one  hour  ;  and,  as  an  instance,  we 
will  take  the  earth  and  Jupiter.  In  Fig.  86  let  E  F  be 
the  path  described  by  the  earth  in  one  hour,  and  E  e  the 
path  in  a  straight  line  which  the  earth  would  have  de- 
scribed in  one  hour  if  nothing  had  disturbed  it ;  and  let 
J  K  be  the  path  described  by  Jupiter  in  one  hour ;  and 


ASTRONOMY. 


219 


Jj  the  path  Jupiter  would  have  described  in  one  hour  if 
nothing  had  disturbed  it.  Then  e  F  is  the  space  through 
which  the  sun's  attraction  has  drawn  the 
earth  in  one  hour,  and  /  K  the  space 
through  which  the  sun's  attraction  has 
drawn  Jupiter  in  one  hour.  We  wish  to 
find  the  ratio  of  e  F  toy  K.  Taking  C 
E  as  95,000,000  miles,  the  circumfer- 
ence of  the  earth's  orbit  is  596,900,000 
miles,  which  the  earth  describes  in  365.26 
days;  and  therefore  the  line  Ee,  which 
is  the  earth's  motion  in  one  hour,  is 
68,091  miles.  Adding  the  square  of 
C  £  to  the  square  of  E  e,  and  extracting 
the  square  root  of  the  sum,  we  find  that 
C  e  is  95,000,024.402  miles ;  and  there- 
fore e  F,  the  space  through  which  the 
sun  draws  the  earth  in  an  hour,  is  24.402 
miles.  For  Jupiter,  C  J  is  494,000,000 
miles ;  the  circumference  of  its  orbit 
is  therefore  3,104,000,000  miles;  which  is  described  in 
4,332.62  days ;  therefore  Jj\  the  motion  in  one  hour,  is 
29,850  miles ;  and  the  length  of  Cjt  found  in  the  same 
manner,  is  494,000,000.9019  miles;  and  j K,  the  space 
through  which  the  sun  draws  Jupiter  in  one  hour,  is  0.9019 
miles. 

The  distances  through  which  these  planets  are  drawn 
towards  the  sun  are  therefore  in  the  ratio  of  24.402  to 
0.9019.  But  if  we  compute,  from  the  rule  of  the  inverse 
square  of  the  distances,  what  would  be  the  proportion  of 
the  force  of  the  sun  on  the  earth  to  the  force  of  the  sun 
on  Jupiter,  we  find  that  it  is  the  proportion  of  24.402  to 
0.9024.  These  proportions  may  be  regarded  as  exactly 
the  same,  the  trifling  difference  between  them  arising 
mainly  from  the  circumstance  that  we  have  used  only  round 


220  ASTRONOMY. 

numbers  for  the  distances  of  the  two  planets  from  the  sun. 
It  is  true,  then,  for  these  two  planets  that  the  strength  of 
the  sun's  attraction  is  inversely  proportional  to  the  square 
of  the  distance  of  the  attracted  body  from  the  sun. 

192.  The  Paths  of  all  the  Planets  and  their  Satellites  are 
curved  by  Gravity.  —  If  we  should  compare  any  two  plan- 
ets in  the  same  way,  we  should  arrive  at  the  same  conclu- 
sion. 

In  fact  it  has  been  demonstrated  that  whenever  the  rule 
known  as  Kepler's  third  law  (42)  holds,  —  namely,  that 
"  the  squares  of  the  periodic  times  of  several  bodies  mov- 
ing round  a  central  body  are  proportional  to  the  cubes  of 
the  distances  of  the  several  bodies  from  that  central  body," 
—  then  it  will  be  found,  by  a  process  exactly  similar  to 
that  which  we  have  gone  through,  that  the  effects  of  the 
central  body's  attraction  at  the  different  distances  are  in- 
versely as  the  squares  of  the  distances.  Now,  this  law  was 
discovered  by  Kepler,  long  before  the  theory  of  gravita- 
tion was  invented,  to  hold  in  regard  to  the  times  and  dis- 
tances of  the  planets  in  their  revolutions  round  the  sun. 
Moreover,  in  regard  to  the  four  satellites  of  Jupiter,  the 
same  law  holds.  For  we  are  able  without  difficulty  to 
observe  their  periodic  times ;  we  are  able  also  to  ascertain 
their  angular  distance  from  Jupiter ;  and  from  this,  know- 
ing the  distance  of  Jupiter  from  the  earth  in  miles,  we  can 
compute  the  distance  of  each  satellite  from  Jupiter  in 
miles.  We  thus  find  that  the  squares  of  their  times  are 
proportional  to  the  cubes  of  their  distances.  Consequently 
the  attraction  of  Jupiter  upon  his  several  satellites  is  in- 
versely proportional  to  the  squares  of  their  distances  from 
him.  In  like  manner  it  is  found  that  the  attraction  of 
Saturn  upon  his  eight  satellites  is  inversely  proportional 
to  the  squares  of  their  distances  from  him ;  and,  so  far  as 
we  can  examine,  the  same  law  holds  with  regard  to  the 
attraction  of  Uranus  and  Neptune  on  their  satellites. 


ASTRONOMY. 


221 


Thus,  for  every  body  which  we  know  around  which  other 
bodies  revolve,  the  force  of  attraction  of  the  central  body 
on  the  different  bodies  that  revolve  round  it  is  inversely 
proportional  to  the  squares  of  their  distances. 

193.  Gravity  causes  the  Planets  and  their  Moons  to  move 
in  Ellipses.  —  Kepler  also  discovered  that  the  planets  do 
not  move  in  circles  but  ellipses.     Hence  their  distance 
from  the  sun  varies.     We  have  now  found  it  true  that  the 
attraction  of  the  central  body  upon  the  bodies  revolving 
about  it  follows  the  law  of  the  inverse  squares  of  the  dis- 
tances ;  does  this  law  hold  in  the  case  of  each  planet  as  its 
distance  from  the  sun  varies  ? 

We  have  already  seen  that  when  a  planet  moves  in  an 
ellipse,  the  deflecting  force  must  be  directed  to  the  focus 
of  the  ellipse,  in  order  that  a  line  drawn  from  that  focus  to 
the  planet  may  describe  equal  areas  in  equal  times.  Since 
the  planets  are  thus  constantly  pulled  towards  the  sun,  and 
since  they  at  times  really  approach  him,  it  would  seem 
that  they  would  be  unable  to  recede  from  him  again. 

194.  The  Resolution  of  Forces.  —  Before  we  show  how  it 
is  that  a  planet  can  thus   recede  from  the  sun,  we  must 
explain  what  is  called  the  resolution  of  forces.     This  may 
be  illustrated  by  the  apparatus  represented  in  Figure  87. 

Fig.  87. 


Suppose  A  and  B  to  be  two  pulleys,  fixed  upon  an  up- 
right frame,  and  suppose  two  cords  to  pass  over  them, 


222  ASTRONOMY. 

carrying  the  two  weights,  C  and  Z>,  at  their  ends  ;  and 
where  they  meet  at  E  let  a  third  cord  be  attached,  carry- 
ing the  weight  -F;  then  the  tension  or  pull  produced  by 
this  one  weight  F,  acting  at  the  point  £,  supports  two 
tensions  in  different  directions  acting  at  the  same  point, 
namely,  the  tension  .produced  by  the  weight  C  acting  in 
the  direction  E  A,  and  the  tension  produced  by  the  weight 
D  acting  in  the  direction  E  B.  Thus  we  may  say,  that 
one  pull  in  the  direction  E  F  exerts  two  pulls  in  different 
directions,  A  E  and  B  E,  for  it  keeps  the  two  cords 
strained  so  as  to  support  the  two  other  weights.  We  may 
say,  on  the  other  hand,  that  these  two  outside  weights,  C 
and  Z>,  support  the  middle  one.  The  three  pulls  of  the 
cords  keep  the  point  E  in  equilibrium ;  but  they  will  sup- 
port it  only  in  one  position,  according  to  the  amount  of 
weight  which  is  hung  to  each  cord.  If  we  put  another 
weight  upon  C,  the  position  of  the  point  E  and  the  direc- 
tion of  the  cords  will  immediately  change.  Regarding 
the  action  of  the  two  tensions  in  the  directions  E  A, 
E  B,  as  supporting  the  one  tension  in  the  direction  E  F, 
this  may  be  considered  as  an  instance  of  the  combination 
of  forces ;  and  regarding  the  one  tension  in  the  direc- 
tion E  F,  as  supporting  two  in  the  directions  A  J5,  E  B, 
this  may  be  considered  as  an  instance  of  the  resolution 
of  forces,  the  one  force  in  the  direction  E  F  being  re- 
solved into  two  forces  in  the  directions  A  E,  BE,  and 
producing  in  all  respects  the  same  effects  as  two  forces  in 
the  directions  A  E,  B  E. 

Having,  then,  a  force  in  any  one  direction,  we  may  re- 
solve it  into  two  forces  acting  in  any  two  directions  suited 
to  the  nature  of  the  case,  and  we  may  use  those  two  forces 
instead  of  the  one  original  force. 

195.  We  can  now  see  how  it  is  that  when  a  planet  has 
once  begun  to  approach  to  the  sun,  it  can  recede  again 
from  it.  Suppose,  in  Figure  88,  a  planet  is  moving  from  /, 


ASTRONOMY. 


223 


through  M,  towards  L.     The  attraction  of  the  sun  pulls  it 
the  direction  of  the  line  MS.     Upon  the  principle  of 


in 


the  resolution  of  forces,  we  may  consider  the  force  in  the 
direction  of  MS  to  be  resolved  into  two,  one  of  which  is  in 


the  direction  of  JVM,  perpendicular  to  the  orbit,  and  the 
other  is  in  the  direction  of  O  M,  parallel  to  that  part  of  the 
orbit.  Now  that  part  of  the  force  which  is  in  the  direction 
JVM,  perpendicular  to  the  orbit,  makes  the  orbit  curved. 
But  that  part  which  acts  in  the  direction  of  O  M,  parallel 
to  the  orbit,  produces  a  different  ef-  Fig.  89. 

feet ;  it  accelerates  the  planet's  mo- 
tion in  its  orbit.  Thus,  in  going 
from  /  towards  Z,  the  planet  is  made 
to  go  quicker  and  quicker.  If  the 
diagram  (Figure  88)  be  turned  in 
such  a  manner  that  MS  is  vertical, 
S  being  downwards,  the  planet  is 
under  the  same  circumstances  as  a  ball  rolling  down  a  hill. 
If  a  ball  is  going  down  a  hill,  as  at  M,  Figure  89,  the  force 
of  gravity,  which  is  in  the  direction  MS,  may  be  resolved 


224  ASTRONOMY. 

into  two  parts,  one  of  which  acts  in  the  direction  IV  M, 
perpendicular  to  the  hillside,  and  merely  presses  the  ball 
towards  the  hill ;  the  other  acts  in  the  direction  O  Af, 
making  it  go  the  faster  down  the  hill.  In  this  manner,  as 
long  as  the  planet  goes  from  k  through  M  towards  Z,  it  is 
going  quicker  and  quicker.  It  has  been  explained  above 
(176),  that  the  curvature  of  a  planet's  orbit,  or  the  curvature 
of  the  path  of  a  cannon-ball,  depends  upon  two  circum- 
stances ;  one  is  the  velocity  with  which  it  is  going,  and 
the  other  is  the  force  which  acts  to  bend  its  path.  The 
greater  its  speed,  the  less  its  path  is  curved.  Conse- 
quently, as  the  planet  is  going  so  fast  in  the  neighbor- 
hood of  K,  its  orbit  may  be  very  little  curved  there,  even 
though  the  sun  is  there  pulling  it  with  a  very  great  force. 
The  effect  of  this  is,  that  the  planet  passes  the  sun  and 
begins  to  recede  from  it.  But  it  does  not  recede  perpet- 
ually. Suppose,  for  instance,  that  it  has  reached  the  point 
M' ;  the  force  of  the  sun  in  the  direction  M'S  may  be  re- 
solved into  two,  in  the  directions  N'M',  O M' ,  of  which 
the  former  only  curves  the  orbit,  while  the  latter  retards 
the  planet  in  its  movement  in  the  orbit.  Therefore,  as 
the  planet  recedes  from  the  sun,  it  goes  more  and  more 
slowly,  till  at  last  its  velocity  may  be  diminished  so  much, 
that  the  power  of  the  sun,  reduced  as  it  is  there,  is  enabled 
to  bring  it  back  again.  Thus  the  planet  goes  on  in  its  orbit, 
alternately  approaching  to,  and  receding  from,  the  sun. 

196.  In  Figure  £8,  let  KA  and  ka  be  the  path  in  a 
straight  line  which  the  planet  would  describe  in  an  hour  in 
those  parts  of  its  orbit :  then  will  A  B  and  a  b  be  the  dis- 
tance which  the  planet  is  drawn  towards  the  sun  in  an  hour 
in  each  of  those  positions.  Now,  by  a  somewhat  difficult 
mathematical  investigation,  it  can  be  shown  that  the  lines 
A  B  and  a  b  stand  in  the  inverse  ratio  of  the  squares  of  the 
distances  S  K  and  S k,  and  this  is  found  to  be  true  of  the 
planet  at  any  two  positions  in  its  orbit.  We  therefore  con- 


ASTRONOMY.  225 

elude,  that  when  any  body  moves  in  an  elliptical  orbit  round 
a  certain  body  situated  in  the  focus  of  this  ellipse,  the  de- 
flecting force,  exerted  by  the  central  body,  varies  in  the 
inverse  proportion  of  the  squares  of  the  distances  between 
the  two  bodies. 


GRAVITY   ACTS   BETWEEN   THE   SUN   AND 
COMETS. 

197.  The  Parabolic  Motion  of  Comets. — There  is,  how- 
ever, another  remarkable  class  of  bodies  of  which  we  have 
already  spoken  ;  namely,  the  comets.  Can  the  curved  form 
of  their  paths  be  accounted  for  on  the  supposition  that 
they  are  drawn  toward  the  sun  by  the  same  force  as  the 
planets  ?  A  few  of  the  comets,  as  has  been  stated  (157),  are 
now  known  to  move  in  very  long  ellipses,  and  to  return 
periodically  to  our  sight.  Of  course  their  motion  can  be 
accounted  for  in  the  same  way  as  that  of  the  planets ;  but, 
in  Newton's  time,  the  idea  of  a  periodical  comet  was  wholly 
unknown  ;  and  it  is  now  certain  that  many  of  the  comets, 
after  visiting  the  sun,  never  return  to  him  again. 

But  since  curvature  of  the  path  of  a  planet  depends  both 
upon  the  force  which  draws  it  towards  the  sun  and  upon  its 
velocity,  we  can  readily  see  that  the  velocity  of  a  planet 
might  be  so  great  that  its  path  would  never  be  bent  around 
enough  to  bring  it  back  to  the  sun.  Newton  showed,  by 
an  investigation  similar  to  that  made  in  the  case  of  an 
elliptical  orbit,  that  a  body  subject  to  the  attraction  of  a 
central  body  (as  the  sun)  might,  if  the  Fig  ^ 

force  varied  inversely  as  the  square  of 
the  distance,  describe  the  curve  called 
the  parabola;  but  no  other  law  of  force 
would  account  for  the  description  of 
such  a  curve.  The  form  of  the  para- 
bola is  represented  in  Figure  90,  C  be- 

10*  o 


226  ASTRONOMY. 

ing  the  sun ;  and  this  curve,  it  is  evident,  possesses  two 
of  the  peculiarities  which  distinguish  the  motions  of 
comets ;  it  comes  very  near  to  the  sun  at  one  part,  and 
it  goes  off  to  an  indefinitely  great  distance  at  other  parts. 
Now,  when  Newton  had  found  out  that  the  same  laws  of 
gravitation  which  were  established  from  the  consideration 
of  elliptical  motion  would  account  for  motion  in  a  parab- 
ola, he  began  to  try  whether  the  parabola  would  not  repre- 
sent the  motion  of  a  comet.  It  was  found,  that  by  taking 
a  parabola  of  certain  dimensions,  and  in  a  certain  position, 
the  motions  of  the  comet  which  had  been  observed  most 
accurately  could  be  represented  with  the  utmost  precision. 
Since  that  time,  the  same  investigation  has  been  repeated 
for  hundreds  of  comets ;  and  it  has  been  found,  in  every 
instance,  that  the  comet's  movements  could  be  exactly 
represented  by  supposing  it  to  move  in  a  parabola  of  proper 
dimensions  and  in  the  proper  position,  the  sun  being  always 
situated  at  a  certain  point  called  the  focus  of  the  parabola. 
This  investigation  tends  most  powerfully  to  confirm  the  law 
of  gravitation  ;  showing  that  the  same  moving  body,  which 
at  one  time  is  very  near  to  the  sun,  and  at  another  time  is 
inconceivably  distant  from  it,  is  subject  to  an  attraction  of 
the  sun  varying  inversely  as. the  square  of  the  distance. 

GRAVITY  ACTS  AMONG  ALL  THE   HEAVENLY 
BODIES. 

198.  The  Moorfs  Perturbations. — We  \have  seen  that 
the  sun  attracts  the  earth.  Does  it  also  attract  the  moon  ? 
If  so,  as  these  bodies  are  always  either  at  different  dis- 
tances from  the  sun,  or  lie  in  different  directions  from  the 
sun,  they  will  be  differently  attracted  by  him ;  and  hence 
their  relative  motions  will  be  disturbed.  We  find  that  these 
motions  are  thus  disturbed,  giving  rise  to  what  are  called 
perturbations.  These  perturbations  were  discovered  from 


ASTRONOMY. 


227 


observation  long  before  the  theory  of  gravitation  was  in- 
vented. One  of  the  first  triumphs  of  the  theory  was  their 
complete  explanation.  We  shall  attempt  here  to  explain 
only  the  one  which  is  called  the  Moon's  Variation. 

In  Figure  91,  suppose  E  to  be  the  earth,  M'  M"  M'" 
M""  the  moon's  orbit,  and  C  the  sun.     The  sun,  by  the 


Fig. 


law  of  gravitation,  attracts  bodies  which 
are  near  with  greater  force  than  those 
which  are  far  distant  from  it.  There- 
fore, when  the  moon  is  at  M'  the  sun 
attracts  the  moon  more  than  the  earth, 
and  tends  to  pull  the  moon  away  from 
the  earth.  When  the  moon  is  at  M"' 
the  sun  attracts  the  earth  more  than 
the  moon,  and  therefore  tends  to  pull 
the  earth  from  the  moon,  producing  the 
same  effect  as  at  M'  or  tending  to  sep- 
arate them.  When  the  moon  is  at  M" 
the  force  of  the  sun  on  the  moon  is  nearly  the  same  as  the 
force  of  the  sun  upon  the  earth,  but  it  is  in  a  different  di- 
rection. If  the  sun  pulls  the  earth  through  the  space  E  e, 
and  if  it  also  pulls  the  moon  through  the  same  space  M"m, 
these  attractions  tend  to  bring  the  earth  and  the  moon 
nearer  together,  because  the  two  bodies  are  moved  as  it 
were  along  the  sides  of  a  wedge  which  grows  narrower 
and  narrower.  Thus,  at  M'  and  M'"  the  action  of  the 
sun  tends  to  separate  the  earth  and  the  moon,  and  at  M" 
and  M""  the  action  tends  to  bring  the  earth  and  the 
moon  together. 

One  might  perhaps  infer  from  this  that  the  moon's  orbit 
is  elongated  in  the  direction  M'  M'" -,  but  the  effect  is 
exactly  the  opposite.  The  fact  really  is,  that  the  moon's 
orbit  is  elongated  in  the  direction  M"  M"".  And  it  can 
easily  be  shown  that  it  must  be  so.  The  moon,  we  will 
suppose,  is  travelling  from  M""  to  M'.  All  this  time  the 


228  ASTRONOMY. 

sun  is  attracting  her  more  than  the  earth,  and  therefore 
increasing  her  velocity  till  she  reaches  M' '.  When  she  is 
passing  from  M'  to  M"  the  sun  is  pulling  her  back,  and 
her  velocity  is  diminished  till  she  reaches  M".  From  this 
point  her  velocity  increases  again  till  she  reaches  M'",  and 
then  diminishes  again  till  she  reaches  M"" .  Therefore, 
when  the  moon  is  nearest  to  the  sun,  and  farthest  from  the 
sun,  she  is  moving  with  the  greatest  velocity ;  when  she  is 
at  those  parts  of  her  orbit  at  which  her  distance  from  the 
sun  is  equal  to  the  earth's  distance  from  the  sun,  she  is 
moving  with  the  least  velocity.  We  have  learned  that  the 
curvature  of  the  orbit  depends  on  two  considerations.  One 
is  the  velocity  \  and  the  greater  the  velocity  is,  the  less  the 
orbit  will  be  curved.  The  other  is  the  force ;  and  the  less 
the  force  is,  the  less  the  orbit  will  be  curved.  Since,  then, 
the  velocity  is  greatest  at  M'  and  M"',  and  the  force  di- 
rected to  the  earth  is  least  (because  the  sun's  disturbing 
force  there  diminishes  the  earth's  attraction),  the  orbit 
must  be  the  least  curved  there.  At  M"  and  M""  the  ve- 
locity has  been  considerably  diminished  ;  the  force  which 
draws  the  moon  towards  the  earth  is  greatest  there  (be- 
cause the  sun's  disturbing  force  there  increases  the  earth's 
attraction),  and  therefore  the  orbit  must  be  most  curved 
there.  The  only  way  of  reconciling  these  conclusions  is 
by  saying  that  the  orbit  is  lengthened  in  the  direction 
M"  M"" ;  a  conclusion  opposite  to  what  we  should  have 
supposed  if  we  had  not  investigated  closely  this  remark- 
able phenomenon.  It  will  easily  be  understood  that  the 
amount  of  this  effect  is  modified  in  some  degree  by  the 
change  which  the  earth's  attraction  undergoes  in  conse- 
quence of  the  change  of  the  moon's  distance,  (the  earth's 
attractive  force  varying  inversely  as  the  square  of  the 
moon's  distance,)  but  still  the  reasoning  applies  with  per- 
fect accuracy  to  the  kind  of  alteration  which  is  produced 
in  the  moon's  orbit. 


ASTRONOMY.  229 

This  particular  inequality  was  discovered  by  Tycho 
de  Brahe  before  gravitation  was  known ;  and  it  was  ex- 
plained by  Newton  as  a  result  of  gravitation.  There  are 
other  perturbations,  even  more  important  than  this,  which 
were  discovered  before  gravitation  was  known,  and  which 
were  most  fully  and  accurately  explained  by  gravitation. 

199.  The  Mutual  Perturbations  of  the  Planets.  —  Again, 
it  is  found  that  there  are  disturbances  in  the  motions  of 
the  planets  generally ;  and  these  disturbances  can  be  ex- 
plained only  by  supposing  that  every  planet  attracts  every 
other  planet,  and  that  therefore  the  motions  of  the  planets 
are  not  exactly  the  same  as  if  only  the  sun  attracted  them. 
These  disturbances  are  exceedingly  complicated.  There 
is  one  kind,  however,  of  which  possibly  some  notion  may 
be  given.  They  are  the  most  remarkable  in  Jupiter  and 
Saturn.  There  are  many  books, 
written  as  late  as  the  beginning 
of  the  present  century,  in  which 
the  motions  of  Jupiter  and  Saturn 
are  spoken  of  as  irreconcilable  with 
the  theory  of  gravitation.  It  was 
one  of  the  grand  discoveries  of  La 
Place  that  the  great  disturbances 
of  those  two  planets  are  caused  by 
what  is  called  the  "inequality  of 
long  period,"  requiring  some  hundreds  of  years  to  go 
through  all  its  changes.  »  • 

Let  Figure  92  represent  the  orbits  of  Jupiter  and  Sat- 
.urn.  They  are  both  ellipses,  and  the  positions  of  their 
axes  do  not  correspond.  Now,  the  thing  which  La  Place 
pointed  out  as  affecting  the  perturbations  of  these  planets 
is  one  which  applies  more  or  less  to  several  other  planets ; 
namely,  that  the  periodic  times  of  Jupiter  and  Saturn  are 
very  nearly  in  the  proportion  of  two  small  numbers,  2  to  5. 

Inasmuch  as  these  periodic  times  are  in  the  proportion 


230  ASTRONOMY. 

of  2  to  5,  it  follows  that,  while  Saturn  is  describing  two 
thirds  of  a  revolution  in  its  orbit,  Jupiter  is  describing 
almost  exactly  five  thirds  of  a  revolution  in  its  orbit.  If, 
therefore,  the  two  planets  have  been  in  conjunction,  then 
about  twenty  years  afterwards  Saturn  has  described  two 
thirds  of  a  revolution,  and  Jupiter  a  whole  revolution  and 
two  thirds,  and  the  planets  will  be  in  conjunction  again, 
but  not  in  the  same  parts  of  their  orbits  as  before,  but  in 
parts  farther  on  by  two  thirds  of  a  revolution.  Thus,  in 
Figure  92,  suppose  i  i  to  be  the  place  of  the  first  conjunc- 
tion of  which  we  are  speaking.  Saturn  describes  two  thirds 
of  his  orbit  as  far  as  the  figure  2.  Jupiter  goes  on  describ- 
ing a  whole  revolution  and  two  thirds  of  a  revolution,  and 
arrives  at  the  same  time  at  the  figure  2  in  his  orbit,  and 
the  planets  are  in  conjunction  at  2  2.  Saturn  goes  on  de- 
scribing two  thirds  of  the  orbit  again,  and  comes  to  figure 
3.  Jupiter  goes  on  describing  a  whole  revolution  and  two 
thirds  of  another,  and  he  comes  to  figure  3,  and  they  are 
in  conjunction  there.  The  next  time  they  are  in  conjunc- 
tion at  figure  4,  the  next  at  figure  5,  and  the  next  at  figure 
6,  and  so  on.  These  conjunctions  occur  in  this  manner 
from  the  circumstance  that  the  periodic  times  are  nearly 
in  the  proportion  pf  2  to  5  ;  there  are  three  points  of  the 
orbit  at  nearly  equal  distances,  at  which  the  conjunctions 
occur. 

But  we  will  suppose  that  they  occurred  exactly  at  three 
equidistant  points,  and  that  time  after  time  they  happened 
exactly  at  the  same  points.  It  is  plain  that  in  that  case 
there  would  be  a  remarkable  effect  of  the  disturbances, 
particularly  at  those  parts  of  the  orbit  i  i,  2  2,  3  3,  etc., 
where  Jupiter  and  Saturn  are  nearer  to  each  other  than  at 
other  times.  They  are  very  large  planets ;  each  of  them 
larger  than  all  the  rest  of  the  solar  system,  except  the  sun. 
They  exercise  very  great  attractive  force  each  upon  the 
other ;  and  therefore  they  would  disturb  each  other  in  a 


ASTRONOMY.  231 

very  great  degree,  if  their  conjunctions  occurred  exactly 
"at  the  same  place. 

Now,  these  conjunctions  do  not  occur  exactly  at  the 
same  place.  The  periodic  times  are  nearly  in  the  propor- 
tion of  2  to  5,  but  not  exactly  in  that  proportion.  Conse- 
quently their  places  of  conjunction  travel  on,  until  after  a 
certain  time  the  points  of  conjunction  of  the  series  i,  4,  7, 
etc.,  would  have  travelled  on  until  they  met  the  series  3,  6, 
9,  etc.  A  period  of  not  less  than  nine  hundred  years  is 
required  for  this  change. 

Now,  so  long  as  three  conjunctions  take  place  at  any 
definite  set  of  points,  the  effect  on  the  orbits  is  of  one 
kind.  As  they  travel  on,  the  effect  is  of  another  descrip- 
tion (because,  from  the  eccentricity  of  their  orbits,  the  dis- 
tance between  the  planets  at  conjunction  is  not  the  same), 
and  so  they  go  on  changing  slowly  until  the  points  of  the 
series  i,  4,  7,  etc.,  are  extended  so  far  as  to  join  the  series 
3,  6,  9,  etc.  ;  and  then  the  conjunctions  of  the  two  planets 
occur  at  the  same  points  of  their  orbits  as  at  first,  and  the 
effect  of  each  planet  in  disturbing  the  other  is  the  same  as 
at  first ;  and  thus  we  have  the  same  thing  recurring  over 
and  over  again  for  ages.  During  one  half  of  each  period 
of  nine  hundred  years,  the  effect  that  one  planet  has  upon 
the  other  is,  that  its  orbit  has  been  slowly  changing ;  and 
then,  during  the  other  half,  it  comes  back  to  what  it  was 
before.  Suppose  that,  during  half  the  nine  hundred  years, 
one  planet  has  been  causing  the  other  to  move  a  little 
quicker,  and  that,  during  the  other  half  of  that  nine  hun- 
dred years,  it  has  been  causing  it  to  move  a  little  slower ; 
although  that  change  maybe  extremely  small  as  regards  the 
velocity  of  the  planets,  yet,  as  that  velocity  has  four  hun- 
dred and  fifty  years  to  produce  its  effect  in  one  way,  and 
an  equal  time  to  produce  its  effect  in  the  opposite  way,  it 
does  produce  a  considerable  irregularity.  If  the  place  of 
Saturn  be  calculated  on  the '  supposition  that  its  periodic 


232  ASTRONOMY. 

time  is  always  the  same,  then  at  one  time  its  real  place  will 
be  behind  its  computed  place  by  about  one  degree,  and 
four  hundred  and  fifty  years  later  its  real  place  will  be  be- 
fore its  computed  place  by  about  one  degree,  so  that  in 
four  hundred  and  fifty  years  it  will  seem  to  have  gained 
two  degrees.  The  corresponding  disturbances  of  Jupiter 
are  not  quite  so  large. 

These  are  the  most  remarkable  of  all  the  planetary  dis- 
turbances, their  magnitude  being  greater  than  any  other, 
fon  account  of  the  magnitude  of  the  planets,  and  the  eccen- 
tricity of  their  orbits.  There  are,  however,  others  of  the 
same  kind.  One  of  these  depends  upon  the  circumstance, 
that  eight  times  the  periodic  time  of  the  earth  is  very  near- 
ly equal  to  thirteen  times  the  periodic  time  of  Venus. 

We  have  attempted  to  explain  only  one  limited  class  of 
perturbations.  There  are  some  which  may  be  described 
as  a  slow  increase  and  decrease  of  the  eccentricities  of  the 
orbits,  and  a  slow  change  in  the  direction  of  the  longer 
axes  of  the  orbits  ;  but  there  are  others  of  which  no  intelli- 
gible account  can  be  given  in  an  elementary  book. 

200.  The  Calculation  of  the  Amount  of  these  Perturba- 
tions.—  In  order,  however,  to  bring  these  theories  into 
actual  calculation,  it  is  necessary  to  know  not  only  the 
general  tendency  of  the  disturbances,  but  also  their  actual 
magnitude.  In  the  perturbations  produced  by  the  earth, 
by  Jupiter,  and  by  Saturn,  there  is  no  difficulty  in  doing 
this.  We  have  shown  (191)  that  we  can  calculate  the 
number  of  miles  through  which  the  earth's  attraction  draws 
the  moon  in  one  hour.  We  know  also  (179)  that  the 
earth's  attraction  draws  every  body  at  the  earth's  surface 
through  the  same  space  in  the  same  time ;  so  that  a  ball  of 
lead  and  a  feather  will  fall  to  the  ground  with  equal  speed, 
if  the  resistance  of  the  air  is  removed.  We  say,  therefore, 
that  the  earth's  attraction  would  draw  a  planet  through  the 
same  space  as  the  moon,  provided  the  planet  were  at  the 


ASTRONOMY.  233 

moon's  distance ;  and,  for  the  greater  distance  of  the  planet. 
we  must,  by  the  law  of  gravitation,  diminish  that  space  in 
the  inverse  proportion  of  the  square  of  the  distance.  We 
have  already  learned  (192)  how  to  compute  the  space 
through  which  the  sun  draws  a  planet  in  one  hour ;  and 
therefore  the  problem  now  is,  to  compute  the  motion  of  a 
planet,  knowing  exactly  how  far,  and  in  what  direction, 
the  sun  will  draw  it  in  one  hour,  and  also  knowing  exactly 
how  far,  and  in  what  direction,  the  earth  will  draw  it  in 
one  hour. 

In  like  manner  we  can,  from  observations  of  Jupiter's 
satellites,  compute  how  far  Jupiter  draws  one  of  his  satel- 
lites in  one  hour,  and  therefore  how  far  Jupiter  would 
draw  a  planet  at  the  same  distance  in  one  hour :  and  then 
by  the  law  of  gravitation  we  can  compute  (by  the  propor- 
tion of  inverse  squares  of  the  distances)  how  far  Jupiter 
will  draw  a  planet  at  any  distance  in  one  hour ;  and  this  is 
to  be  combined,  in  computation,  with  the  space  through 
which  the  sun  will  draw  the  planet  in  one  hour.  In  like 
manner,  by  similar  observations  of  Saturn's  satellites,  and 
similar  reasoning,  we  can  find  how  far  Saturn  will  draw  any 
planet  in  one  hour,  and  we  can  combine  this  with  the  space 
through  which  the  sun  would  draw  it  in  one  hour.  Thus 
we  are  enabled  to  compute  completely  the  perturbations 
which  these  three  planets  produce  in  any  other  planets. 

20 1.  Do  the  Planets'  Motions,  as  computed  with  these  Dis- 
turbances, agree  with  what  we  see  in  actual  Observation  ?  — 
They  do  agree  most  perfectly.  Perhaps  the  best  proof 
which  can  be  given  of  the  care  with  which  astronomers 
have  looked  to  this  matter,  is  the  following.  The  meas- 
ures of  the  distances  of  Jupiter's  moons  in  use  till  within 
the  last  sixteen  years,  had  not  been  made  with  due  ac- 
curacy; and,  in  consequence,  the  perturbations  produced 
by  Jupiter  had  all  been  computed  too  small  by  about  one 
fiftieth  part.  So  great  a  discordance  manifested  itself 


234  ASTRONOMY. 

* 

between  the  computed  and  the  observed  motions  of  some 
of  the  planets,  that  many  of  the  German  astronomers 
expressed  themselves  doubtful  of  the  truth  of  the  law  of 
gravitation.  Airy,  the  Astronomer  Royal  of  England,  was 
led  to  make  a  new  set  of  observations  of  Jupiter's  satel- 
lites, and  discovered  that  these  bodies  were  farther  from 
Jupiter  than  was  supposed,  that  the  space  through  which 
Jupiter  drew  them  in  an  hour  was  greater  than  was  sup- 
posed, and  that  the  perturbations  ought  to  be  increased 
by  about  one  fiftieth  part.  On  using  the  corrected  per- 
turbations, the  computed  and  the  observed  places  of  the 
planets  agreed  perfectly. 

The  motions  of  our  moon  are  sensibly  disturbed  by  the 
planet  Venus.  An  irregularity,  which  had  been  discovered 
by  observation,  and  had  puzzled  all  astronomers  for  fifty 
years,  was  explained  a  short  time  ago  by  Professor  Han- 
sen,  of  Gotha,  on  the  theory  of  gravitation,  as  a  very  curi- 
ous effect  of  the  attraction  of  Venus. 

202.  The  Theory  of  Gravitation  holds  good  throughout  the 
known  Universe.  —We  thus  see  that  the  theory  of  gravita- 
tion holds  good  as  far  as  the  solar  system  extends.  We 
have  learned,  moreover,  that  the  binary  stars  which  have 
been  observed  to  revolve  about  one  another  all  move  in 
elliptical  orbits.  Hence,  they  must  act  upon  one  another 
with  a  force  which  varies  inversely  as  the  square  of  the 
distance.  Hence,  the  law  of  gravitation  seems  to  hold,  as 
far  as  we  are  able  to  extend  our  observations  into  space. 

SUMMARY. 

From  the  rotating  of  a  wheel,  and  the  vibrating  of  a 
free  pendulum  in  a  vacuum,  we  infer  that  a  moving  body 
will  continue  to  move  in  a  straight  line  and  with  a  uniform 
velocity  until  it  is  acted  upon  by  some  force.  (172.) 

By  means  of  a  projecting  machine  and  Atwood's  ma- 


ASTRONOMY.  235 

chine,  we  find  that  a  moving  body,  when  acted  upon  by 
gravity  alone,  will,  at  any  given  time,  be  just  as  far  from  the 
point  which  it  would  have  readied  had  it  been  left  to  itself, 
as  it  would  have  been  had  it  been  at  rest  at  that  point  in  the 
first  place  and  been  acted  upon  by  gravity  alone  during  the 
same  time.  (174,  175-) 

By  the  falling  of  bodies  in  a  vacuum,  and  by  the  pendu- 
lum, we  find  that  gravity  acts  upon  a  body  near  the  earth 
with  a  force  whose  intensity  varies  directly  as  the  mass  of 
the  body,  and  is  sufficient  to  draw  it  from  a  state  of  rest 
one  hundred  and  ninety-three  inches  in  a  second.  (179, 
1 88,  189.) 

The  planets  and  their  moons  all  describe  curved  paths. 
Hence  they  must  be  acted  upon  by  some  force.  (173.) 

They  all  describe  equal  areas  in  equal  time.  Hence  the 
force  which  curves  their  paths  must,  in  the  case  of  the 
planets,  be  directed  toward  the  sun,  and,  in  the  case  of 
the  moons,  toward  the  planet  about  which  they  revolve. 

(177-) 

At  the  distance  of  the  moon,  gravity,  if  its  intensity  di- 
minishes as  the  square  of  the  distance  increases,  will  cause 
a  body  to  fall  towards  the  earth  .05305  of  an  inch.  It  is 
found  by  computation  that,  when  allowance  is  made  for 
disturbing  causes  which  are  known  to  exist,  the  moon  is 
drawn  toward  the  earth  exactly  this  distance  each  second. 
Hence  we  conclude  that  gravity  acts  between  the  earth  and 
the  moon  with  a  force  whose  intensity  varies  ^directly  as  the 
mass  of  the  body  acted  upon,  and  inversely  as  the  square 
of  its  distance.  (190.) 

It  is  found  by  computation  that,  during  a  given  time,  all 
the  planets  are  drawn  toward  the  sun,  a  distance  which 
varies  inversely  as  the  square  of  their  distance  from  him. 
Hence  they  must  be  acted  upon  by  a  force  which  varies 
directly  as  their  mass  and  inversely  as  the  square  of  their 
distance  from  the  sun.  It  is  also  found  that  the  planets 


236  ASTRONOMY. 

must  be  acted  upon  by  such  a  force,  in  order  that  they 
may  move  in  ellipses.  From  this  we  conclude  that  gravity 
acts  between  the  sun  and  the  planets.  For  a  like  reason 
we  conclude  that  gravity  acts  between  the  planets  and  their 
moons.  (191-196.) 

The  comets  describe  elliptical  and  parabolic  orbits. 
Hence  they  must  be  acted  upon  by  gravity.  (197.) 

The  perturbations  of  the  moon  show  that  gravity  must 
act  between  the  sun  and  the  moon,  as  well  as  between  the 
sun  and  the  earth,  and  the  earth  and  the  moon.  (198.) 

The  perturbations  of  the  planets  can  all  be  exactly  ac- 
counted for  by  supposing  that  each  acts  upon  every  other 
with  a  force -varying  directly  as  the  mass  and  inversely  as 
the  square  of  the  distance  of  these  bodies.  Hence  we  con- 
clude that  gravity  acts  among  all  the  bodies  of  the  solar 
system.  (199-201.) 

The  binary  and  multiple  stars  revolve  about  one  another 
in  elliptical  orbits.  Hence  we  conclude  that  gravity  acts 
between  stars  and  stars  as  well  as  among  the  members  of 
our  solar  system.  (202.) 

The  planets  not  only  describe  ellipses  which  differ  from 
one  another  in  their  eccentricity  and  their  inclination  to 
the  ecliptic,  but  the  path  described  by  each  planet  is  con- 
stantly undergoing  changes  in  each  of  these  particulars. 
These  changes  go  on  increasing  in  one  direction  for  a 
certain  length  of  time,  when  they  again  begin  to  diminish. 
It  has  been  shown  by  mathematical  investigations  that 
these  changes  can  in  no  case  reach  such  a  point  as  to 
break  up  the  present  order  of  our  system,  provided  that 
system  be  acted  upon  by  no  external  force,  but  that  they 
all  repeat  themselves  in  cycles  which  are  in  some  cases 
of  enormous  length. 

These  changes  of  very  long  period  are  often  called 
secular  changes. 


ASTRONOMY.  237 

GRAVITY  ACTS  UPON  THE  PARTICLES  OF 
MATTER. 

203.  We  have  now  learned  that  gravity  acts  upon  all 
the  heavenly  bodies  with  a  force  varying  directly  as  their 
masses,  and   inversely  as  the  squares  of  their  distances 
from  one  another.     Does  gravity  act  upon  these  bodies  as 
wholes,  or  upon  the  particles  of  which  they  are  composed  ? 

204.  The  Tides.  —  If  the  force  acting  between  the  sun 
and  the  earth,  and  between  the  moon  and  the  earth,  acts 
upon  the  particles  of  which  the  earth  is  made  up,  those 
particles  which  are  nearest  the  sun  or  moon  ought  to  be 
pulled  more  strongly  than  those  which  are  farther  away, 
and,  if  they  were  free  to  move,  they  ought  to  be  drawn 
away  from  those  behind  them.     But  the  particles  of  water' 
have  great  freedom  of  motion  among  themselves.     Are  the 
waters  of  the  ocean  heaped  up  under  the  sun  and  moon, 
as  they  should  be  if  gravity  acts,  not  upon  the  earth  as 
a  whole,  but  upon  the  particles  of  which  it  is  composed  ? 

Now  it  is  well  known  that  tides  exist  in  the  ocean,  and 
that  the  tidal  wave  follows  the  moon  in  her  daily  round. 
The  particles  of  water  nearest  the  moon  are  then  drawn 

Fig-  93- 


238 


ASTRONOMY. 


away  from  those  behind  them,  thus  giving  rise  to  the  tides. 
It  is  only  the  mutual  attraction  among  the  particles  of 
which  the  earth  is  composed,  that  keeps  these  particles 
from  being  drawn  entirely  away  from  the  earth. 

On  the  side  of  the  earth  opposite  the  moon,  the  particles 
of  the  water  are  dra.wn  less  strongly  than  those  of  the  solid 


ea*rth  which  are  nearer  the  moon.  For  this  reason  the 
solid  part  of  the  earth  is  here  drawn  away  from  the  water. 
This  gives  rise  to  a  tidal  wave  also  on  the  part  of  the 
ocean  opposite  the  moon. 

The  tides  follow  the  moon  generally,  but  not  entirely. 


ASTRONOMY. 


239 


They  do  not  follow  the  time  of  the  moon's  meridian  pas- 
sage by.  the  same  interval  at  all  times  ;  and  they  are  much 
larger  shortly  after  new  moon  and  full  moon  than  at  other 
times.  From  a  careful  examination  of  all  the  phenomena 
of  tides,  it  appears  that  they  may  be  most  accurately  rep- 
resented by  the  combination  of  two  independent  tides,  the 
larger  produced  by  the  moon  (as  shown  in  Figure  93),  and 

Fig.  95- 


the  smaller  produced  by  the  sun.  When  these  two  tides 
are  added  together,  they  make  a  very  large,  tide  (as  shown 
in  Figure  94),  which  is  called  a  spring-tide;  but  when  the 
high  water  produced  by  the  sun  is  combined  with  the  low 
water  produced  by  the  moon,  and  the  low  water  produced 
by  the  sun  is  combined  with  the  high  water  produced  by 
the  moon  (see  Figure  95),  a  small  tide  is  produced,  which 
is  called  a  neap-tide.  We  conclude  then  that  the  force  of 
gravity  which  acts  between  the  sun  and  the  earth,  and  be- 
tween the  moon  and  the  earth,  does  not  act  upon  the  earth 


240  ASTRONOMY. 

as  a  whole,  but  upon  each  particle  of  which  the  earth  is 
composed. 

205.  The  Spheroidal  Form  of  the.  Earth.  — Another  im- 
portant fact  bearing  upon  the  theory  of  gravitation  is  the 
spheroidal  form  of  the  earth. 

We  have  seen  in  Part  First  of  this  work  (138)  that  the 
materials  of  the  earth  are  evidently  the  result  of  burning. 
The  heat  developed  by  this  combustion  must  have  been 
sufficient  to  reduce  the  whole  mass  to  the  liquid  state.  It 
then  slowly  solidified  at  the  surface,  forming  the  rocks  and 
soil.  There  is  the  best  of  evidence  that  the  interior  of 
the  earth  is  still  a  molten  mass.  Portions  of  this  molten 
matter  are  often  poured  forth  from  the  craters  of  volca- 
noes, which  act  as  so  many  safety-valves  to  relieve  the 
pent-up  forces  within.  Again,  in  deep  mines  the  tempera- 
ture, as  we  descend,  is  found  to  increase  at  a  rate  which 
shows  that  a  few  miles  below  the  surface  the  heat  must  be 
sufficient  to  fuse  all  known  rocks. 

The  earth  was,  then,  without  doubt,  once  a  liquid  mass  ; 
and,  obeying  the  tendency  of  all  liquids,  would  have  shaped 
itself  into  a  perfect  sphere,  had  nothing  interfered  with  this 
tendency.  But  we  have  already  seen  that  the  earth  is  not 
a  perfect  sphere,  but  is  flattened  at  the  poles,  and  protrudes 
at  the  equator.  How  can  this  form  be  explained  ? 

Fig.  96. 


When  the  hoop,  in  Figure  96,  is  made  to  rotate  rapidly 
on  its  axis,  it  flattens  in  the  direction  of  the  axis,  and 
bulges  out  in  the  direction  at  right  angles  to  this  axis.  To 


ASTRONOMY.  241 

understand  why  the  hoop  bulges  out  in  this  way  we  must 
remember  the  first  law  of  motion,  namely,  that  when  a 
body  is  once  put  in  motion  it  will  move  on  a  straight 
line  if  it  can.  No  matter  in  what  way  the  part  of  the  hoop 
a  is  put  in  motion,  it  Las  no  tendency  to  move  in  a  circle, 
but  will  move  in  a  horizontal  straight  line,  if  this  is  possi- 
ble. By  motion  in  a  straight  line,  this  part  a  would  go  far- 
ther and  farther  from  the  central  bar.  In  order  to  keep  it 
at  the  same  distance  from  the  central  bar,  a  restraining 
force  is  necessary.  The  term  centrifugal  force  has  been 
used  to  express  the  tendency  of  the  various  parts  of  the 
hoop  to  get  farther  off  from  the  central  bar.  This  term  is 
not  a  good  one,  since  there  is  in  reality  no  force.  Cen- 
trifugal tendency  would  be  less  objectionable. 

The  form  that  the  hoop  assumes  depends  upon  this 
centrifugal  tendency,  and  upon  the  restraining  force  of 
the  hoop  which  keeps  'the  parts  from  moving  in  a  straight 
line.'  The  less  this  restraining  force,  and  the  greater  the 
centrifugal  tendency,  the  more  flattened  the  hoop  becomes. 

In  the  same  way,  the  flattened  form  of  the  earth  must  be 
accounted  for  by  the  centrifugal  tendency  of  its  parts 
when  in  the  liquid  state,  developed  by  its  rotation  on  its 
axis,  together  with  the  restraining  force  which  binds  the 
particles  of  the  earth  together. 

Now,  it  has  been  found  by  careful  investigation,  that  the 
present  form  of  the  earth  can  be  accounted  for  by  the 
action  of  the  centrifugal  tendency,  on  the  supposition  that 
every  particle  of  the  earth  attracts  every  other  particle  with 
a  force  varying  in  the  inverse  ratio  of  the  square  of  the  dis- 
tance. We  have,  then,  an  evidence  here,  that  every  parti- 
cle of  matter  in  a  body  attracts  every  other  particle  in  the 
inverse  ratio  of  the  square  of  the  distance ;  and,  in  the 
case  of  tides,  an  evidence  that  the  sun  and  moon  attract 
every  particle  of  the  earth  in  the  inverse  ratio  of  the 
square  of  the  distance. 

ii  p 


242  ASTRONOMY. 

206.  The  Precession  of  the  Equinoxes  is  caused  by  Gravity. 
—  The  precession  of  the  equinoxes  has  already  been  de- 
scribed (70).  According  to  the  theory  of  gravitation,  the 
sun's  attraction  is  stronger  at  A  (Figure  97)  than  at  C, 
since  A  is  nearer  than  C.  Hence  the  sun  is  always  acting 
on  A,  the  part  nearest  to  it,  as  if  it  were  pulling  it  away 
from  the  earth's  centre.  If  it  pulled  the  centre  and  the 
surface  of  the  earth  equally,  it  would  not  tend  to  separate 
•them  ;  but  since  it  pulls  the  former  at  A  more  than  the 
latter,  it  tends  to  draw  it  away  from  the  centre  towards  S. 

In  like  manner,  as  the  sun  pulls  the  centre  more  power- 
fully than  it  pulls  B,  it  tends  to  separate  them,  not  by  pull- 
ing the  opposite  side  B  from  the  centre,  but  by  pulling  the 
centre  from  the  opposite  side  B.  The  general  effect  of 
the  sun's  attraction,  therefore,  as  tending  to  affect  the  dif- 
ferent parts  of  the  earth,  is  this  :  that  it  tends  to  pull  the 
nearest  parts  towards  the  sun,  and  to  push  the  most  dis- 
tant parts  from  the  sun. 

If  the  earth  were  a  perfect  sphere,  this  would  be  a  mat- 
ter of  no  consequence :  it  would  produce  tides  of  the  sea, 
but  it  would  not  affect  the  motion  of  the  solid  parts.  But 
the  earth,  as  we  have  seen,  is  not  a  sphere  ;  it  is  flattened 
like  a  turnip,  or  has  the  form  of  a  spheroid.  Moreover, 
the  axis  of  the  earth  is  not  perpendicular  to  the  ecliptic; 
the  earth's  equator,  at  all  times  except  the  equinoxes,  is 
inclined  to  the  line  joining  the  earth's  centre  with  the  sun. 

Let  us  now  consider  the  position  of  the  earth  at  the 
winter  solstice,  shown  in  Figure  97.  The  North  Pole  is 
away  from  the  sun  ;  the  South  Pole  is  turned  towards 
the  sun.  This  spheroidal  earth,  at  this  time,  has  its  pro- 
tuberance, not  turned  exactly  towards  the  sun,  but  raised 
above  it.  As  we  have  seen,  the  attraction  of  the  sun  is 
pulling  the  part  D  of  the  earth  more  strongly  than  it  pulls 
the  centre.  The  immediate  tendency  of  that  action  is  to 
bring  the  part  D . towards  #,  supposing  a  to  be  in  the  plane 


ASTRONOMY.  243 

Fig.  97. 


passing  through  the  centre  of  the  sun  and  the  centre  of  the 
earth.  This  is  because  the  force  pulling  D  towards  the  sun 
is  equivalent  to  two  other  forces  :  one  in  the  direction  of 
CD,  tending  to  pull  D  from  C;  and  the  other  acting  at 
right  angles  to  this  direction,  tending  to  carry  D  towards  a. 
In  like  manner,  as  the  sun  attracts  the  centre  of  the  earth 
more  than  it  attracts  the  protuberance  E,  which  amounts 
to  the  same  thing  as  pushing  the  protuberance  E  away 
from  the  sun,  there  is  a  tendency  to  bring  E  towards  b. 
The  immediate  tendency  of  the  sun's  pulling,  therefore,  is 
so  to  change  the  position  of  the  earth  that  its  axis  will  be- 
come more  nearly  perpendicular  to  the  plane  of  the  eclip- 
tic ;  but  this  tendency  to  change  the  inclination  of  the  axis 
is  entirely  modified  by  the  rotation  of  the  earth.  Undoubt- 
edly, if  the  earth  were  not  revolving,  and  if  the  earth  were 
of  a  spheroidal  shape,  the  attraction  of  the  sun  would  tend 
to  pull  it  into  such  a  position  that  the  axis  of  the  earth 
would  become  perpendicular  to  the  line  S  C ;  or  (if  in  the 
position  of  the  winter  solstice)  it  would  beconte  perpendic- 
ular to  the  plane  of  the  ecliptic ;  but,  in  consequence  of 
the  rotation  of  the  earth,  the  attraction  produces  a  wholly 
different  effect.  Let  us  consider  the  motion  of  a  mountain 
in  the  earth's  protuberance,  which,  passing  through  the 
point  c  on  the  distant  side  of  the  earth,  would,  in  the  semi- 
revolution  of  half  a  day,  describe  the  arc  c  D  e,  if  the  sun 
did  not  act  on  it  (c  and  e  being  the  points  at  which  this 
circle  c  D  e  intersects  the  plane  of  the  ecliptic,  or  the  plane 


244  ASTRONOMY. 

of  the  circle  a  b  that  passes  through  the  sun).  While  the 
protuberant  mountain  is  describing  the  path  c  D  e  it  is  con- 
stantly nearer  to  the  sun  than  the  earth's  centre  is ;  the  dif- 
ference of  the  sun's  action  therefore  tends  to  pull  that 
mountain  towards  S,  and  therefore  (as  it  cannot  be  sepa- 
rated from  the  earth)  to  pull  it  downwards,  'giving  to  the 
earth  a  tilting  movement ;  it  will,  therefore,  through  the 
mountain's  whole  course,  from  <r,  make  it  describe  a  lower 
curve  than  it  would  otherwise  have  described,  and  will 
make  it  describe  the  curve  cfg  instead  of  the  curve  c  D  e. 
The  result  of  this  is,  that,  as  it  mounts  from  ctof,  the  sun's 
downward  pull  draws  it  towards  the  ecliptic,  and  conse- 
quently renders  its  path  less  steep  than  it  would  otherwise 
be.  At  /  it  will  be  a  very  little  lower  than  it  would  other- 
wise have  been  at  D  ;  but  as  the  sun's  downward  pull  still 
acts  upon  it  till  it  comes  to  g,  the  steepness  of  its  path  be- 
tween yand^is  increased  more  than  belongs  naturally  to 
its  elevation  at  f,  and  becomes  in  fact  the  same  as  it  was 
at  f,  or  very  nearly  so  ;  so  that  the  inclination  of  the  path 
to  the  plane  of  the  circle  a  b  is  the  same  as  at  first.  But, 
instead  of  crossing  the  circle  a  b  at  <?,  it  will  cross  at^.-  in 
other  words,  it  will,  in  consequence  of  the  sun's  action, 
come  to  the  crossing  place  earlier  than  it  would  have  come 
had  the  sun  not  acted.  In  the  remaining  half  of  its  rota- 
tion, from  g  towards  c  again,  it  is  farther  from  the  sun  than 
the  earth's  centre  is ;  therefore  the  sun's  action  does,  in 
fact,  tend  to  push  it  away  (as  already  explained) ;  and  as  it 
cannot  be  separated  from  the  earth,  this  force  tends  to  push 
the  mountain  upwards  towards  the  circle  £,  tilting  the  earth 
in  the  same  direction  as  before ;  the  mountain,  therefore, 
in  this  part^will  move  in  a  path  higher  than  it  would  have 
moved  in  without  the  sun's  action,  and  therefore  it  will 
come  to  its  intersection  with  the  circle  a  b  sooner  than  it 
would  if  not  subject  to  that  action.  The  inclination  of  its 
path  (just  as  in  the  former  half  of  its  rotation)  will  not  be 


ASTRONOMY.  245 

altered.  Thus  the  effect  produced  by  this  action  of  the 
sun,  in  both  halves  of  the  rotation  of  this  mountain  is,  that 
it  comes  to  the  place  of  intersection  with  the  plane  of  the 
circle  a  b,  or  with  the  plane  of  the  ecliptic,  sooner  than  it 
otherwise  would.  And  whatever  number  of  points  or 
mountains  in  the  protuberant  part  of  the  earth  we  consider, 
we  shall  find  the  same  effect  for  every  one ;  and  therefore, 
the  effect  of  the  sun's  action  upon  the  entire  protuberance 
will  be  the  same;  that  is,  its  inclination  to  the  circle  a  b, 
or  the  plane  of  the  ecliptic,  will  not  be  altered ;  but  the 
places  in  which  it  crosses  that  plane  will  be  perpetually 
altering  in  such  a  direction  as  to  meet  the  direction  of 
rotation  of  the  earth. 

We  have  spoken  as  if  the  protuberance  were  the  only 
part  to  be  considered.  In  reality,  this  protuberance  is 
attached  to  the  remaining  spherical  part  of  the  earth ;  but 
the  action  of  the  sun  on  the  different  masses  of  that  spheri- 
cal part  balances  exactly  ;  so  that  we  need  not  consider  the 
sun's  action  upon  it  at  all.  The  only  effect,  therefore,  of 
that  spherical  part  will  be  to  impede  the  motion  which  the 
protuberant  part  would  otherwise  have  :  not  to  destroy  it, 
but  to  diminish  it. 

On  the  whole,  therefore,  the  effect  of  the  sun's  action  on 
the  spheroidal  earth  will  be,  that  the  points  at  which  the 
earth's  equator  intersects  the  plane  of  the  ecliptic  move 
very  slowly  in  the  direction  opposite  to  that  in  which  the 
earth  revolves ;  but  the  inclination  is  not  altered. 

All  that  I  have  said  here  applies  to  the  position  of  the 
earth  at  the  winter  solstice.  But  if  we  consider  the  earth 
at  the  summer  solstice,  on  the  opposite  side  of  the  sun,  we 
shall  find  that  the  effect  of  the  sun's  action  is  exactly  the 
same.  At  the  equinoxes,  the  plane  of  the  earth's  equator 
passes  through  the  sun,  and  then  the  sun's  action  does  not 
tend  to  tilt  the  earth  at  all,  and  consequently  does  not  tend 
to  alter  the  position  of  its  equator ;  but  at  all  other  times 


246  ASTRONOMY. 

the  sun's  action  produces  a  motion,  greater  or  less,  of  the 
intersection  of  the  earth's  equator  with  the  plane  of  the 
ecliptic,  in  a  direction  opposite  to  that  of  the  earth's  rota- 
tion. And  this  is  the  motion  called  the  precession  of  the 
equinoxes. 

It  is  to  be  observed  that  the  principal  part  of  this  pre- 
cession is  produced,  not  by  the  sun,  but  by  the  moon. 
The  moon's  mass  is  not  a  twenty  millionth  part  of  the 
sun's,  but  she  is  four  hundred  times  as  near  as  the  sun. 
Still  she  does  not  pull  the  earth  as  a  mass  with  more  than 
a  hundred  and  twentieth  part  of  the  sun's  force.  But  since 
the  difference  of  the  distances  of  the  different  parts  of  the 
earth  from  the  moon  bears  a  greater  proportion  to  the 
whole  distance  than  in  the  case  of  the  sun,  the  effect  of 
the  moon  in  pulling  the  nearer  parts  of  the  earth  from  the 
earth's  centre,  and  in  pushing  the  more  distant  parts  of 
the  earth  from  the  earth's  centre,  is  about  treble  the  effect 
of  the  sun. 

We  now  see  that  the  precession  of  the  equinoxes  is  per- 
fectly explained  by  the  supposition  that  the  sun  attracts 
every  particle  of  the  earth,  and  that  it  cannot  be  explained 
without  making  this  supposition. 

SUMMARY. 

Every  particle  of  matter  in  our  solar  system  acts  upon 
every  other  particle  with  a  force  varying  inversely  as  the 
square  of  their  distance  from  one  another. 

This  supposition  is  necessary  to  explain  the  tides  (204), 
the  spheroidal  form  of  the  earth  (205),  and  fa&  precession  of 
the  equinoxes.  (206.) 

The  tides  result  from  the  struggle  between  the  attraction 
of  gravity  among  the  particles  of  the  earth,  and  that  be- 
tween the  particles  of  the  earth  and  those  of  the  sun  and 
moon.  (204.) 


ASTRONOMY.  247 

The  spheroidal  form  of  the  earth  resulted  from  the  strug- 
gle between  the  attraction  of  gravity  among  the  particles 
of  the  earth,  and  the  centrifugal  tendency  of  the  particles 
of  the  earth  in  the  neighborhood  of  the  equator,  when  the 
earth  was  in  the  liquid  state.  (205). 

The  precession  of  the  equinoxes  is  the  result  of  the  struggle 
between  the  attraction  of  the  sun  and  moon  upon  the 
earth's  equatorial  protuberance,  and  the  tendency  of  this 
ring  always  to  rotate  in  the  same  plane.  (206). 

HOW    TO    FIND    THE    WEIGHT    OF    THE 
HEAVENLY    BODIES. 

207.  The  Weight  of  the  Sun  and  Planets.  —  Having  thus 
established  the  law  of  gravitation,  we  next  inquire  after  the 
strength  of  this  force.     Of  course  we  know  nothing  about 
the  absolute  strength  of  this  or  any  force.     We  only  know 
their  relative  strength,   and  we  must  compare  the  force 
exerted  between  two  bodies  with  the  force  exerted  between 
the  earth  and  a  pound  of  water.     We  want,  first,  to  find 
the  weight  of  the  earth ;   that  is,  to  find  how  the  force  act- 
ing between  any  given  body  and  a  pound  of  water  com- 
pares with  the  force  acting  between  this  same  body  and 
the  earth. 

208.  The  Schehallien  Experiment.  —  The  first  experiment 
for  ascertaining  this  was  made  at  the  Schehallien  moun- 
tain, in  Scotland.      It  was  argued   that  if  the  theory  of 
gravitation  were  true,  —  that  is  to  say,  if  attraction  were 
produced,  not  by  a  tendency  to  the  centre  of  the  earth,  or 
to  any  special  point,  but  to  every  particle  of  the  earth's 
structure,  —  then,  by  the  fundamental  law  of  gravitation,  the 
attraction  of  a  mountain  would  be  a  sensible  thing ;  for  a 
mountain  is  a  part  of  the  earth,  with  this  difference  only, 
that  though  the  mountain  is  small  in  comparison  with  the 
earth,  yet  you  get  so  close  to  the  mountain,  that  its  effect 


248  ASTRONOMY. 

may  be  very  sensible  as  compared  with  the  effect  produced 
by  the  rest  of  the  earth.  Some  parts  of  the  earth  are  eight 
thousand  miles  from  us,  and  their  attraction  will  be  com- 
paratively small.  It  was  therefore  thought  worth  while  to 
ascertain  whether  the  attraction  of  a  mountain,  would  be 
sensibly  felt. 

The  Schehallien  mountain  ranges  east  and  west.  It  was 
possible  to  make  astronomical  observations  on  the  north 
and  south  sides ;  and  it  was  also  possible  to  connect  the 
two  places  of  observation  by  triangulation  (54).  Suppose 

Fig-  95- 


Figure  95  to  represent  a  section  of  the  mountain,  north 
and  south ;  and  JV  the  northern,  S  the  southern  observ- 
ing station.  Observations  were  made  at  JV  and  6*  upon 
stars  with  the  Zenith  Sector  (53).  By  the  use  of  this  in- 
strument the  difference  of  the  directions  of  gravity  at  these 
two  stations  was  found,  exactly  in  the  same  manner  as  the 
difference  of  the  directions  of  gravity  in  the  two  stations 
in  Figure  25. 

The  direction  of  gravity  at  each  station  is  the  result  of 
the  gravity  of  the  whole  earth  (as  considered  for  a  moment 
independently  of  the  mountain),  combined  with  the  attrac- 
tion of  the  mountain.  Supposing  that  at  JV,  if  there  were 
no  mountain,  the  direction  of  gravity  would  be  N e;  then 
introducing  the  supposition  of  the  mountain,  the  attraction 
of  the  mountain  would  pull  the  plumb-line  sideways  to- 


ASTRONOMY.  249 

wards  the  centre  of  the  mountain,  and  the  direction  of  the 
gravity  would  be  N  E.  And  in  like  manner,  supposing 
that  if  there  were  no  mountain,  the  direction  of  the  gravity 
at  S  would  be  S  F;  then,  introducing  the  mountain,  the 
effect  of  its  attraction  is  to  pull  the  plumb-line  towards  the 
centre  of  the  mountain,  and  the  direction  of  gravity  would 
be  Sf.  We  see,  then,  the  effect  of  the  mountain.  At  JV 
the  direction  of  gravity  is  N  E  instead  of  N  e^  and  at  S 
the  direction  of  gravity  is  Sf  instead  of  S  F,  —  that  is  to 
say,  the  two  directions  which  are  taken  by  the  plumb-line 
of  the  Zenith  Sector,  make  a  greater  angle  than  they  would 
if  the  mountain  were  not  there. 

Now  we  know  the  general  dimensions  of  the  earth  ;  we 
know  what  the  inclination  of  the  plumb-line  at  N  and  S 
would  be  if  there  were  no  mountain  in  the  case.  If,  then, 
we  can  find  the  distance  from  our  observing  station  at  N 
to  that  at  S,  then  we  can  tell  from  that  distance  how  much 
the  directions  of  the  plumb-line  at  Nand  S  would  be  in- 
clined if  there  were  no  mountain  ;  and  we  can  compare 
that  inclination  with  the  inclination  observed  by  means  of 
the  Zenith  Sector. 

Accordingly,  the  observations  were  made  in  exactly  the 
same  manner  as  those  made  for  determining  the  figure  of 
the  earth  (53-56).  The  Zenith  Sector  was  carried  to  IV, 
and  certain  stars  were  observed ;  the  Zenith  Sector  was 
then  carried  to  S,  and  the  same  stars  were  observed  at 
that  place.  By  means  of  these  observations  of  the  stars, 
the  actual  inclinations  of  the  plumb-line  at  the  two  places 
were  found.  The  next  thing  done  was  to  carry  a  survey 
by  triangulation  across  the  mountain.  This  was  done  in 
the  most  careful  way  in  which  the  best  surveyors  of  the 
time  could  accomplish  the  task.  The  result  was,  that  the 
distance  between  the  stations  was  found  to  be  such,  that, 
supposing  there  were  no  mountain  in  the  case,  the  in- 
clination of  the  two  plumb-lines  ought  to  be  41  seconds, 
n* 


250  ASTRONOMY. 

It  was  found,  from  the  observations  by  the  Zenith  Sec- 
tor, that  the  inclination  of  the  plumb-lines  actually  was 
53  seconds. 

The  difference  between  the  two  was  the  effect  of  the 
mountain.  The  mountain  had  pulled  the  plumb-line  at 
one  station  in  one  direction,  and  at  the  other  station  in  the 
opposite  direction,  to  such  a  degree,  that  the  two  plumb- 
lines,  instead  of  making  an  angle  of  41  seconds,  made  an 
angle  of  53  seconds ;  or,  in  other  words,  the  sum  of  the 
effects  of  the  two  attractions  of  the  mountain,  on  opposite 
sides,  was  twelve  seconds. 

The  next  thing  was,  to  draw  from  this  observation  a  de- 
termination of  the  mean  density  of  the  earth.  The  moun- 
tain was  surveyed,  mapped,  levelled,  and  measured,  in 
every  way,  so  completely  that  a  model  of  it  might  have 
been  made ;  it  was  then  (for  the  sake  of  calculation)  con- 
ceived to  be  divided  into  prisms  of  various  forms :  the  at- 
traction of  every  one  of  these  was  computed,  on  the  sup- 
position that  the  mountain  had  the  same  density  as  the 
mean  density  of  the  earth  ;  and  by  means  of  this,  the  at- 
traction of  the  whole  mountain  was  found  on  the  same 
supposition. 

Thus  it  was  found,  that,  if  the  density  of  the  mountain 
had  been  the  same  as  the  mean  density  of  the  earth,  the 
sum  of  the  effects  of  the  attractions  of  the  mountain  at  JV 
and  *S  would  have  been  about  ^'37  part  of  gravity.  But 
the  observed  sum  of  effects  was  12  seconds,  which  cor- 
responds to  -pnhri-  Part  of  gravity.  Hence  the  density  of 
the  mountain  is  only  about  f  of  the  earth's  mean  density ; 
or  the  earth's  mean  density  is  nearly  double  the  moun- 
tain's density.  The  nature  of  the  rocks  composing  the 
mountain  was  carefully  examined,  and  their  density  as 
compared  with  that  of  water  was  ascertained;  and  thus 
the  mean  density  of  the  earth  was  found  to  be  something 
less  than  five  times  the  density  of  water. 


ASTRONOMY.  25 1 

209.  The  Cavendish  Experiment.  —  After  this  another 
set  of  experiments  was  made ;  first  by  Mr.  Henry  Caven- 
dish, a  rich  man,  much  attached  to  science  (from  whom 
the  experiment  of  which  we  are  speaking  received  the 
name  of  the  Cavendish  Experiment) ;  afterwards  by  a  Dr. 
Reich;  and  finally,  in  a  very  much  more  complete  way, 
by  Mr.  Francis  Baily,  as  the  active  member  of  a  commit- 
tee of  the  Astronomical  Society  of  London,  to  whom  funds 
were  supplied  by  the  British  Government. 

The  shape  in  which  the  apparatus  is  represented,  in 
Figure  96,  is  that  in  which  it  was  used  by  Mr.  Baily. 
There  are  two  small  balls,  A,  B>  (generally  about  two' 


inches  in  diameter,)  carried  on  a  rod  A  C  J3,  suspended  by 
a  single  wire  D  £,  or  by  two  wires  at  a  small  distance  from 
each  other.  By  means  of  a  telescope,  the  positions  of 
these  balls  were  observed  from  a  distance.  It  was  of  the 
utmost  consequence  that  the  observer  should  not  go  near, 
not  only  to  prevent  his  shaking  the  apparatus,  but  also 
because 'the  warmth  of  the  body  would  create  currents  of 
air  that  would  disturb  everything  very  much,  even  though 
the  balls  were  enclosed  in  double  boxes,  lined  with  gilt 
paper,  to  prevent  as  much  as  possible  the  influence  of  such 


252  ASTRONOMY. 

currents.  When  the  position  of  the  small  balls  had  been 
observed,  large  balls  of  lead,  F,  G,  about  twelve  inches  in 
diameter,  which  moved  upon  a  turning  frame,  were  brought 
near  to  them ;  but  still  they  were  separated  from  each 
other  by  half  a  dozen  thicknesses  of  wooden  boxes,  so  that 
no  effect  could  be  produced  except  by  the  attraction  of 
the  large  balls.  Observations  were  then  made  to  see  how 
much  these  smaller  balls  were  attracted  out  of  their  places 
by  the  large  ones.  By  another  movement  of  the  turning 
frame,  the  larger  balls  could  be  brought  to  the  position 
H K.  In  every  case,  the  motion  of  the  small  balls  pro- 
duced by  the  attraction  of  the  larger  ones  was  undeniably 
apparent.  The  small  balls  were  always  put  into  a  state  of 
vibration  by  this  attraction  ;  then  by  observing  the  extreme 
distances  to  which  they  swing  both  ways,  and  taking  the 
middle  place  between  those  extreme  distances,  we  find  the 
place  at  which  the  attraction  of  the  large  balls  would  hold 
them  steady. 

Suppose,  now,  the  attraction  of  the  large  balls  was  found 
to  pull  the  small  balls  an  inch  away  from  their  former  place 
of  rest,  what  amount  of  dead  pull  does  that  show?  In 
order  to  ascertain  this  we  must  compare  the  vibrations  of 
the  balls  with  those  of  an  ordinary  pendulum. 

We  have  seen  that  when  a  pendulum-ball  is  pulled  aside 
and  let  go,  it  begins  to  vibrate.  The  force  of  gravity  act- 
ing upon  the  pendulum-ball  is  resolved  into  two  parts,  one 
of  which  acts  on  the  ball  in  the  direction  of  the  pendulum- 
rod,  and  the  other  sideways.  The  former  of  course  does 
not  affect  the  movement  of  the  pendulum  at  all ;  it  is  the 
latter  which  causes  the  pendulum  to  vibrate.  This  latter 
force  increases  with  the  distance  the  pendulum  is  pulled 
aside,  and  always  bears  the  same  ratio  to  the  weight  of 
the  pendulum-ball  as  the  distance  the  ball  is  drawn  aside 
bears  to  the  length  of  the  pendulum.  As  a  pendulum 
beating  seconds  is  39.139  inches  long,  the  force  which 


ASTRONOMY.  253 

will  pull  it  one  inch  sideways  will  then  be  re/Tire  °f  its 
weight. 

In  the  case  of  the  lead  balls  suspended  by  a  wire,  when 
they  are  pulled  aside  by  the  large  balls,  they  begin  to  vi- 
brate. This  vibration  is  caused  by  the  torsion,  or  twist, 
of  the  wire.  This  torsion  increases  with  the  distance  the 
balls  are  pulled  aside,  precisely  as  the  force  which  causes 
the  pendulum  to  vibrate  increases,  with  the  distance  it  is 
pulled  aside.  Hence  the  balls  will  vibrate  exactly  like  a 
pendulum.  If,  then,  the  balls  vibrate  in  one  second,  and 
are  pulled  aside  one  inch,  the  force  which  pulls  them 
aside  must  bear  the  same  proportion  to  their  weight  that 
the  force  which  pulls  a  seconds  pendulum  one  inch  aside 
.bears  to  the  weight  of  the  pendulum-ball ;  that  is,  it  must 
be  ^.T^  of  their  weight. 

Then  it  is  known,  as  a  general  theorem  regarding  vibra- 
tions, that,  to  make  the  vibrations  twice  as  slow,  we  must 
have  forces  (for  the  same  distances  of  displacement)  four 
times  as  small ;  and  so  in  proportion  to  the  inverse  square 
of  the  times  of  vibration.  Thus  if  balls  or  anything  else 
vibrate  once  in  ten  seconds,  the  dead  pull  sideways  cor- 
responding to  an  inch  of  displacement  is  -£5737?  °f  their 
weight.  So  that,  in  fact,  all  that  we  now  want  for  our  cal- 
culation, is  the  time  of  vibration  of  the  suspended  balls. 
This  is  very  .easily  observed  ;  and  then,  on  the  principles 
already  explained,  there  is  no  difficulty  in  computing  the 
dead  pull  sideways  corresponding  to  a  sideways  displace- 
ment of  one  inch  ;  and  then  (by  altering  this  in  the  pro- 
portion of  the  observed  displacement,  whatever  it  may  be) 
the  sideways  dead  pull  or  attraction  corresponding  to  any 
observed  displacement  is  readily  found.  The  delicacy  of 
this  method  of  observing  and  computing  the  attraction  of 
the  large  balls  may  be  judged  from  the  fact  that  the  whole 
attraction  amounted  to  only  about  2-ff,<jj<j,Tnnr  Part  °f  the 
weight  of  the  small  balls,  and  that  the  uncertainty  in  the 


254  ASTRONOMY. 

measure  of  this  very  small  quantity  did  not  amount  proba- 
bly to  5V  or  s\y  of  the  whole. 

Then  the  next  step  was  this  :  knowing  the  size  of  the 
large  balls  and  their  distances  from  the  small  balls  in  the 
experiment,  and  knowing  also  the  size  of  the  earth,  and 
the  distance  of  the  small'  balls  from  the  centre  of  the  earth, 
we  can  calculate  what  would  be  the  proportion  of  the  at- 
traction of  the  large  balls  on  the  small  balls  to  the  attrac- 
tion of  the  earth  on  the  small  balls  (that  is,  the  weight  of 
the  small  balls),  if  the  leaden  balls  had  the  same  density 
as  the  mean  density  of  the  earth.  It  was  found  that  this 
would  produce  a  smaller  attraction  than  that  computed 
from  the  observations.  Consequently,  the  mean  density 
of  the  earth  is  less  than  the  density  of  lead  in  the  same 
proportion  ;  and  thus  the  mean  density  of  the  earth  is 
found  to  be  5.67  times  the  density  of  water. 

210.  Another  Method  of  finding  the  Weight  of  the  Earth. 
—  It  has  been  found  that  if  the  law  of  universal  gravita- 
tion be  true,  the  attraction  of  the  whole  earth,  considered 
as  a  sphere,  on  a  body  at  its  surface,  is  the  same  as  if  the 
whole  matter  of  the  earth  were  collected  at  its  centre. 
It  has  -also  been  found  that  the  attraction  of  the  earth  on  a 
body  within  its  surface  is  the  same  as  if  the  spherical  shell 
situated  between  the  body  and  the  earth's  surface  were  re- 
moved ;  or  is  the  same  as  if  all  the  matter  situated  nearer 
to  the  earth's  centre  than  the  body  were  collected  at  the 
centre,  and  all  the  matter  situated  at  a  greater  distance 
were  removed. 

If  the  earth  were  of  uniform  density  throughout,  it  would 
follow  from  these  propositions  that  the  force  of  gravity  at 
the  bottom  of  a  mine  would  be  less  than  the  force  at  the 
top.  To  show  this,  suppose  that  the  mine  reached  half- 
way to  the  centre  of  the  earth.  Then  (since  the  volumes 
of  spheres  vary  as  the  cubes  of  their  diameters)  the  quan- 
tity of  matter  nearer  to  the  earth's  centre  than  the  bottom 


ASTRONOMY.  255 

of  the  mine  would  be  only  one  eighth  of  the  whole  quan- 
tity of  matter  in  the  earth.  But  the  attraction  of  a  quantity 
of  matter  at  the  earth's  centre  would  be  more  powerful  on 
a  body  at  the  bottom  of  a  mine  than  on  one  at  the  top,  in 
the  inverse  ratio  of  the  squares  of  the  distances  of  the 
bodies  from  the  earth's  centre ;  that  is,  in  the  present  case, 
in  the  ratio  of  four  to  one.  Hence  the  attraction  on  a 
body  at  the  bottom  of  a  mine  would  be,  on  the  whole,  less 
than  the  attraction  on  a  body  at  the  top,  in  the  ratio  of 
one  to  two. 

If,  however,  the  earth  be  not  of  uniform  density,  but  its 
density  increase  towards  the  centre,  then,  though  the  at- 
tracting mass  which  acts  on  a  body  at  the  bottom  of  the 
mine  be  smaller,  yet  the  diminution  in  the  force  of  gravity 
so  occasioned  may  be  more  than  compensated  by  the  com- 
parative nearness  of  the  attracted  body  to  the  denser  parts 
of  the  earth.  From  the  two  laws  of  the  attraction  of 
spheres,  which  have  been  stated  above,  it  is  possible  to 
calculate  the  ratio  which  the  force  of  gravity  at  the  bottom 
of  the  mine  would  bear  to  that  at  the  top,  on  any  supposi- 
tion we  choose  to  make  as  to  the  ratio  between  the  mean 
density  of  the  earth  and  the  density  at  the  surface ;  so  that, 
if  we  know  one  ratio  we  can  immediately  infer  the  other. 
Now,  pendulum  observations  afford  us  the  means  of  deter- 
mining the  force  of  gravity  at  any  place ;  and  therefore,  if 
the  times  of  vibration  of  a  pendulum  at  the  top  and  bottom 
of  a  mine  be  found,  the  ratio  of  the  force  of  gravity  at  the 
top  to  that  at  the  bottom  may  be  calculated,  and  thence 
the  ratio  of  the  mean  density  of  the  earth  to  that  of  its 
surface. 

The  pendulum  is  made  of  metal ;  it  turns  with  a  hard 
steel  prism,  having  a  very  fine  edge,  upon  plates  of  agate, 
or  some  very  hard  stone.  It  swings  like  the  pendulum  of 
a  clock.  But  it  must  be  observed  that  a  clock  pendu- 
lum will  not  do  for  this  purpose,  because  there  are  other 


256  ASTRONOMY. 

forces  besides  gravity  acting  upon  it ;  that  is  to  say,  the 
clock  weights  acting  through  the  train  of  the  clock  wheels. 
It  is  necessary  to  have  a  detached  pendulum.  Now  we 
wish  to  know  how  many  vibrations  that  pendulum  would 
make  in  a  day. 

In  modern  experiments  of  this  kind,  the  vibrations  of 
the  detached  pendulum  have  been  compared  with  the  vibra- 
tions of  a  clock  pendulum.  The  mode  usually  adopted  is 
this  :  a  detached  pendulum  is  placed  in  front  of  a  clock ; 
a  person  is  watching  with  a  telescope ;  he  watches  when 
the  two  pendulums  are  going  the  same  way ;  he  remarks 
whether  the  vibrations  of  the  detached  pendulum  recur 
faster  or  slower  than  those  of  the  clock  pendulum  ;  he  sees 
that  the  vibrations  separate  more  and  more,  till  the  two 
pendulums  actually  move  in  opposite  ways  ;  after  this,  they 
begin  to  move  more  nearly  in  the  same  way,  and  at  length 
move  exactly  in  the  same  way.  Perhaps  the  number  of 
vibrations  between  these  two  agreements  of  motion  may 
be  500.  If  we  can  determine  the  time  when  the  two  pen- 
dulums swing  the  same  way,  we  find  how  long  it  is  before 
one  pendulum  gains  two  vibrations  upon  the  other.  Then 
suppose  that  the  detached  pendulum  is  going  slower  than 
the  clock  pendulum ;  and  suppose  that  7  J  minutes  elapse 
between  two  agreements  of  motion  of  the  pendulum  :  this 
shows  that  while  the  clock  has  gone  y|  minutes,  or  while 
its  pendulum  has  made  450  vibrations,  the  detached  pen- 
dulum has  made  only  448  vibrations.  Now,  the  clock  is 
going  day  and  night,  and  by  means  of  observation  with  the 
transit  instrument,  we  can  find  how  many  hours,  minutes, 
and  seconds  the  clock  hands  pass  over  in  one  day,  or  how 
many  vibrations  the  clock  pendulum  makes  in  one  day. 
Then,  as  the  detached  pendulum  makes  448  vibrations  for 
every  450  made  by  the  clock  pendulum,  we  find  at  once 
how  many  vibrations  the  detached  pendulum  makes  in 
t\venty-four  hours. 


ASTRONOMY.  257 

Some  corrections  for  the  effect  of  temperature  in  altering 
the  length  of  the  pendulum,  and  for  other  circumstances, 
are  necessary.  The  method  just  described  is  exceedingly 
delicate.  There  is  no  difficulty  in  ascertaining  by  it  the 
number  of  vibrations  which  the  detached  pendulum  will 
make  in  a  day,  with  no  greater  error  than  one  tenth  of  a 
vibration,  or  with  an  error  not  exceeding  one  eight  hundred 
thousandth  part  of  the  whole. 

This  mode  of  determining  the  weight  of  the  earth  was 
put  in  practice  by  Airy,  the  Astronomer  Royal  of  England, 
at  the  Harton  Coal  Pit,  in  the  year  1854.  The  mean  den- 
sity deduced  from  his  observations  is  6.565  times  that  of 
water  :  a  value  considerably  exceeding  that  found  from  the 
Schehallien  and  Cavendish  experiments. 

Each  cubit  foot  of  the  earth  is  thus  found  to  weigh,  on 
an  average,  about  six  times  as  much  as  a  cubic  foot  of 
water.  In  the  earth  there  are  259,800,000,000  cubic  miles, 
and  in  each  cubic  mile  147,200,000,000  cubic  feet.  From 
these  data  the  whole  weight  of  the  earth  may  be  readily 
found. 

211.  The  Weight  of  the  Sun. — We  have  already  seen 
that  the  motion  of  a  body  in  a  second,  when  drawn  by 
gravity,  is  directly  proportional  to  the  force  acting  upon  it 
Remembering  this,  we  can  easily  find  the  weight  of  the 
sun  as  compared  with  that  of  the  earth. 

We  have  found,  in  Figure  85,  that  the  earth  draws  the 
moon  through  10.963  miles  in  one  hour,  the  moon  being 
at  the  distance  of  238,800  miles  from  the  earth  ;  and 
in  Figure  86,  that  the  sun  draws  the  earth  through  24.402 
miles  in  one  hour,  the  earth  being  at  the  distance  of 
95,000,000  miles  from  the  sun.  In  order  to  compare 
these  attractions,  we  must  reduce  them  both  to  the  same 
distance.  If  the  earth  draws  the  moon  through  10.963 
miles  in  an  hour  when  at  the  distance  of  238,800  miles, 
how  far  would  it  draw  the  moon  in  an  hour  if  it  were  at 

Q 


258  ASTRONOMY. 

the  distance  of  95,000,000  miles?  Diminishing  10.963  in 
the  proportion  of  the  inverse  squares  of  the  distances, 
we  find  that  the  earth  would  draw  the  moon  through 
0.00006927  mile  or  4.389  inches  in  an  hour,  if  it  were  at 
the  distance  of  95,000,000  miles.  Comparing  this  with 
24.402  miles,  through  which  the  sun  draws  the  earth  or 
moon  when  at  the  same  distance,  we  find  that  the  sun's 
attraction  is  352,280  times  as  great  as  the  earth's,  and 
therefore,  that  the  sun's  mass  is  352,280  times  as  great  as 
the  earth's. 

We  have  learned  (87)  that  the  sun's  bulk  is  some 
1,400,000  times  as  great  as  the  earth's  bulk.  Therefore 
the  sun's  mean  density  is  only  about  J  of  the  earth's  mean 
density,  or  about  1.4  times  the  density  of  water. 

212.  The  Weight  of  the  Planets.— The  method  which 
has  been  used  above  for  comparing  the  mass  of  the  earth 
with  that  of  the  sun,  is  also  used  for  comparing  the  mass 
of  Jupiter,  Saturn,  Uranus,  or  Neptune,  with  that  of  the 
sun ;  and  in  all  cases  where  the  moons  can  be  easily  ob- 
served, it  can  be  applied  with  very  great  accuracy.  For 
those  planets  which  have  no  moons  there  is  considerable 
uncertainty.  The  only  way  in  which  their  weight  can  be 
determined  is  by  their  disturbance  of  other  planets.  For 
instance,  in  certain  positions,  the  earth  is  disturbed  by 
Mars  a  few  seconds,  say  six  or  eight.  We  compute  what 
would  be  the  amount  of  perturbation  if  the  planet  Mars 
were  as  big,  or  half  as  big,  as  the  earth,  and  we  alter  the 
supposition  till  we  find  a  mass  which  will  produce  pertur- 
bations equal  to  those  which  we  observe.  This  is  the  pro- 
cess of  trial  and  error,  which  has  already  been  described. 
In  this  manner  the  masses  of  Mars  and  Venus  are  deter- 
mined. That  of  Mars  is  not  very  certain  ;  that  of  Venus 
is  more  certain,  —  both  because  it  produces  larger  pertur- 
bations of  the  earth,  and  because  its  attraction  tends  to 
produce  a  continual  change  in  the  plane  of  the  ecliptic, 


ASTRONOMY.  259 

which  in  many  years  amounts  to  a  very  sensible  quantity. 
The  mass  of  Mercury  is  still  very  uncertain.  Lately  at- 
tempts have  been  made  to  deduce  it  from  the  perturba- 
tions which  Mercury  produces  in  the  motions  of  one  of 
the  comets. 

213.  The  Weight  of  the  Moon  obtained  from  the  Tides.  — 
There  is,  however,  one  mass  which  is  more  important  than 
the  others,  and  that  is  the  mass  of  the  moon.     There  are 
several  methods  by  which  this  mass  is  determined. 

One  method  is  by  comparing  the  tides  at  different  times* 
By  comparing  the  spring-tides  with  the  neap-tides,  we  can 
find  the  proportion  of  the  effect  produced  by  the  moon  to 
that  produced  by  the  sun.  Now,  the  tides  are  produced, 
not  by  the  whole  attraction  of  the  moon  and  the  sun  upon 
the  water,  but  by  the  difference  between  their  attraction 
upon  the  water  and  their  attraction  upon  the  mass  of  the 
earth,  by  which  difference  the  moon  (and  also  the  sun) 
draws  the  water  nearest  to  it  away  from  the  earth,  and 
draws  the  earth  away  from  the  water  which  is  farthest  from 
the  moon. 

With  proper  investigation  it  is  possible  to  find,  from  the 
tidal  effects  of  the  sun  and  moon,  the  proportion  of  their 
differences  of  attraction.  And  knowing  this  proportion, 
and  knowing  the  distances  of  the  sun  and  moon,  we  can 
find  the  proportion  of  their  masses. 

214.  Another  Method  of  finding  the  Moon's   Weight. 

In  Figure   100,  suppose   C  to  be  the  sun,.  E  the  earth, 
M  the  moon.     We  have  spoken  continually  of  the  sun's 
attraction  upon  the  earth,  and  of  the  earth's  revolution 
round  the  sun,  as  if  the  sun  were  the  only  body  whose 
attraction  influenced  in  a  material  degree  the  earth's  move- 
ment.    But  in  reality  the  moon  also  acts  in  a  very  sen- 
sible degree  upon  the  earth.     And  the  immediate  effect 
upon   the   motion  of  the  earth   can  be  found.      Draw  a 
line  from  E  to  M,  and  in  this  line  take  the  point  G,  so 


260 


ASTRONOMY. 


that  the  proportion  of  E  G  to  G  M  is  the 
same  as  the  proportion  of  the  weight  of 
M  to  the  weight  of  E ;  or  so  that  if  E 
and  M  were  like  two  balls  fastened  upon 
the  ends  of  a  rod,  they  would  balance  at  G. 
This  point  would  be  their  common  centre 
of  gravity.  Then  investigation  shows  that 
the  motion  of  the  earth  may  be  almost 
exactly  represented  by  saying  that  the  point 
G  travels  round  the  sun  in  an  ellipse,  de- 
scribing areas  proportional  to  the  times 
(according  to  Kepler's  laws),  and  that  the 
earth  E  revolves  round  the  point  G  in  a 
month,  being  always  on  the  side  opposite 
to  the  moon. 

Consequently,  the  direction  in  which  the  earth  would 
be  seen  from  the  sun  (and  therefore  the  direction  in  which 
the  sun  is  seen  from  the  earth)  depends  in  a  certain  degree 
on  the  distance  E  G.  And,  therefore,  if  we  observe  the 
sun  regularly,  and  if  we  compute  where  we  ought  to  see 
the  sun,  according  to  Kepler's  laws,  the  difference  between 
these  two  directions  will  be  the  angle  E  C  G ;  and  know- 
ing the  distance  C  G,  we  can  then  compute  the  length  of 
E  G,  and  the  proportion  which  it  bears  to  G  M;  and  this 
proportion  is  the  same  as  the  proportion  of  the  mass  of 
the  moon  to  the  mass  of  the  earth. 

These  different  methods  agree  very  well  in  giving  the 
result  that  the  mass  of  the  moon  is  about  ¥V  of  the  earth's 
mass. 


ASTRONOMY.  261 


SUMMARY. 

The  earth  weighs  about  six  times  as  much  as  a  globe  of 
water  of  the  same  size  would  weigh. 

The  weight  of  the  earth  can  be  found  in  three  ways  :  — 

(i.)  By  comparing  the  attraction  exerted  by  the  whole 
earth  with  that  exerted  by  a  mountain,  and  then  ascertain- 
ing the  density  of  the  mountain ;  as  in  the  Schehallien  ex- 
periment. (208.) 

(2.)  By  comparing  the  force  exerted  by  the  earth  upon 
two  small  balls  of  lead  with  that  exerted  upon  the  same  by 
two  large  balls  of  lead ;  as  in  the  Cavendish  experiment. 
(209.) 

(3.)  By  observing  the  vibration  of  a  pendulum  at  the 
earth's  surface,  and  at  the  bottom  of  a  deep  mine ;  as  in 
the  Harton  Coal  Pit  experiment.  (210.) 

Knowing  the  weight  of  the  earth,  the  weight  of  the  sun 
can  be  found  by  comparing  the  distance  the  moon  is  drawn 
by  the  earth  in  an  hour  with  the  distance  the  sun  draws 
the  earth  in  the  same  time.  (211.) 

Having  found  the  weight  of  the  sun,  we  can  find  the 
weight  of  any  planet  which  has  moons  by  comparing  the  dis- 
tance they  draw  their  moons  in  an  hour  with  the  distance 
they  themselves  are  drawn  by  the  sun  in  the  same  time. 

The  weight  of  those  planets  which  have  no  moons  can  be 
found  by  the  perturbations  they  cause  in  .the  motions  of 
other  planets.  (212.)  * 

The  weight  of  the  moon  can  be  found  by  comparing  her 
effect  with  that  of  the  sun  in  producing  the  tides  (213),  and 
by  means  of  the  apparent  displacement  of  the  sun,  occa- 
sioned by  the  action  of  the  moon  upon  the  earth.  (214.) 

The  earth  not  only  draws  the  moon  towards  itself,  but  is 
also  itself  drawn  towards  the  moon ;  and  the  moon  does 
not  really  revolve  about  the  earth,  but  both  these  bodies 


262  ASTRONOMY. 

revolve  about  their  common  centre  of  gravity.  This  centre 
of  gravity  is  very  much  nearer  the  earth  than  the  moon, 
because  the  mass  of  the  earth  is  much  greater  than  that  of 
the  moon.  (214.) 

The  same  thing  is  true  of  the  sun  and  the  planets.  He 
not  only  draws  the  planets  towards  himself,  but  is  himself 
drawn  towards  them ;  and  they  do  not  really  revolve  about 
him  as  a  centre,  but  both  they  and  he  revolve  about  their 
common  centre  of  gravity.  Since  the  mass  of  the  sun 
very  much  exceeds  that  of  all  the  planets,  the  common 
centre  of  gravity  of  the  whole  solar  system  lies  within  the 
surface  of  the  sun. 

So,  too,  in  the  binary  and  multiple  stars,  there  is  no  one 
star  about  which  the  others  revolve,  but  each  revolves 
about  the  common  centre  of  gravity  of  the  system.  If 
both  components  of  a  binary  system  have  equal  masses, 
their  common  centre  of  gravity  would  be  midway  between 
them. 

GENERAL   SUMMARY. 

When  a  free  pendulum  is  vibrating  in  any  part  of  the 
earth  except  at  the  equator,  its  direction  of  vibration  ap- 
pears constantly  to  change ;  and  from  this  we  know  that 
the  earth  must  rotate  on  its  axis  from  west  to  east  once 
in  twenty-four  hours. 

The  planets  follow  such  irregular  paths  among  the 
stars  that  their  motion  can  be  explained  only  by  suppos- 
ing that  they  all  describe  ellipses  which  have  the  sun  at 
one  focus ;  and  the  motion  of  the  moons  can  be  explained 
only  on  the  supposition  that  they  describe  ellipses  about 
their  planets. 

The  time  it  takes  the  earth  to  complete  a  revolution 
about  the  sun  is  found  by  direct  observation  ;  and  then, 
by  observing  their  synodical  revolutions,  the  sidereal 
periods  of  the  planets  can  be  computed. 


ASTRONOMY.  263 

The  relative  distances  of  the  earth  and  the  planets  from 
the  sun  are  found  by  observing  the  greatest  elongation  of 
the  inferior  planets,  and  the  daily  retrogression  of  the 
superior  planets  at  the  time  of  their  opposition. 

The  real  distance  from  the  earth  to  the  sun  is  found  by 
observation  of  the  transits  of  Venus,  and  by  measuring 
an  arc  of  the  earth's  meridian. 

Telescopes  which  are  pointed  at  the  moon  from  Green- 
wich and  the  Cape  of  Good  Hope,  differ  in  direction  ; 
and  by  measuring  this  difference  of  direction,  the  dis- 
tance of  the  moon  from  the  earth  is  ascertained. 

When  a  telescope  is  pointed  to  a  fixed  star,  from  oppo- 
site points  of  the  earth's  orbit,  there  is  often  an  appreciable 
difference  in  its  direction.  This  difference  can  be  measured, 
and,  by  means  of  it,  we  can  find  the  distance  of  the  stars. 

All  the  stars  in  the  neighborhood  of  the  constellation 
Hercules  appear  to  be  spreading  away  from  a  point  in  that 
constellation;  and  from  this  we  know  that  our  sun  is 
travelling  through  space  towards  that  point. 

The  stars  are  slowly  changing  their  configurations,  and 
must  therefore  be  in  motion. 

The  sun  is  about  a  million  and  a  half  times  as  large  as 
the  earth ;  he  rotates  on  his  axis  in  about  twenty-five  days ; 
he  is  surrounded  by  an  atmosphere  several  thousand  miles 
in  depth ;  and  his  photosphere  is  probably  a  stratum  of 
clouds  suspended  in  this  atmosphere.  The  spots  on  his 
disc  are  probably  caused  by  the  cooling,  of  portions  of 
these  clouds  by  downward  currents ;  while  the  faculae  are 
caused  by  the  raising  of  other  portions  into  ridges  by  up- 
ward currents. 

The  moon  presents  a  very  rough  and  rugged  surface ; 
and  there  are  indications  of  similar  inequalities  in  the  case 
of  Mercury,  Venus,  and  Mars. 

The  four  inner  planets  are  all  of  moderate  size.  They 
all  have  atmospheres,  and  all  appear  to  rotate  on  their  axes 


264  ASTRONOMY. 

in  about  twenty-four  hours ;  and  of  these,  the  earth  alone 
has  a  moon.  The  four  outer  planets  form  another  group, 
and  differ  strikingly  from  these  in  their  enormous  size, 
their  rapid  rotation  on  their  axes,  and  in  their  complex 
systems  of  satellites.  Between  this  inner  and  outer  group 
of  planets  there  is  a  large  number  of  telescopic  bodies, 
forming  the  well-marked  group  of  the  Minor  Planets. 

Many  of  the  stars  change  their  color  and  their  bright- 
ness. Some  undergo  these  changes  in  short  and  regular 
periods,  and  others  at  long  and  perhaps  irregular  intervals. 

The  vibration  of  a  free  pendulum  in  a  vacuum  can  be 
explained  only  on  the  supposition  that  a  moving  body 
always  tends  to  move  in  a  straight  line  and  with  an  un- 
varying velocity. 

Gravity  has  the  same  effect  upon  a  moving  body  as 
upon  a  body  at  rest. 

Gravity  acting  upon  a  body  near  the  earth  causes  it  to 
fall  from  a  state  of  rest  193  inches  in  a  second. 

Since  the  planets  and  moons  describe  equal  areas  in 
equal  times,  the  force  which  deflects  their  paths  must  be 
directed  in  the  case  of  the  planets  towards  the  sun,  and  in 
the  case  of  the  moons  towards  their  planets. 

On  the  supposition  that  a  stone  at  the  distance  of  the 
moon  would  be  still  acted  upon  by  gravity,  but  with  a  force 
which  diminishes  as  the  square  of  the  distance  from  the 
earth's  centre  increases,  it  would  fall  just  as  far  in  a  unit 
of  time  as  the  moon  is  drawn  towards  the  earth  in  the 
same  time.  We  therefore  conclude  that  gravity  extends  to 
the  moon. 

The  distances  the  planets  are  drawn  towards  the  sun 
in  a  given  time  are  exactly  in  the  inverse  ratio  of  the 
squares  of  their  distances  from  him ;  and  the  force  which 
causes  a  planet  to  describe  an  ellipse  must  vary  inversely 
as  the  square  of  its  distance  from  the  sun.  Hence  we 
conclude  that  gravity  acts  between  the  sun  and  the 
planets. 


ASTRONOMY.  265 

The  perturbations  of  the  planets  can  be  explained  only 
by  the  supposition  that  each  attracts  the  others  with  a 
force  which  varies  directly  as  the  mass  of  the  bodies  acted 
upon,  and  inversely  as  the  square  of  their  distances  from 
one  another.  We  therefore  conclude  that  all  the  members 
of  the  solar  system  are  acted  upon  by  gravity. 

Many  of  the  stars  move  in  elliptical  orbits.  Hence  we 
conclude  that  gravity  acts  among  all  the  heavenly  bodies. 

The  tides,  the  spheroidal  form  of  the  earth,  and  the 
precession  of  the  equinoxes  can  be  explained  only  on  the 
supposition  that  gravity  acts  among  the  particles  of  the 
earth,  and  between  these  and  the  sun  and  moon.  Gravity 
therefore  acts  upon  the  heavenly  bodies,  not  as  wholes, 
but  upon  the  particles  of  which  they  are  composed. 

By  comparing  the  pull  exerted  by  one  piece  of  lead 
upon  another  with  the  pull  exerted  by  the  earth  upon  the 
sun,  we  are  able  to  express  the  pull  of  the  earth  in  pounds. 
The  distance  a  body  is  pulled  from  a  state  of  rest  in  a  sec- 
ond is  directly  proportional  to  the  effective  pull  of  gravity 
acting  upon  it.  The  earth's  gravity  can  then  be  compared 
with  that  of  the  sun  by  comparing  the  distance  the  moon 
is  drawn  through  by  the  earth  in  a  second  with  the  dis- 
tance the  earth  is  drawn  through  in  a  second  by  the  sun. 
The  gravity  of  a  planet  which  has  a  moon  can  be  compared 
with  the  gravity  of  the  sun  by  comparing  the  distance  the 
planet  draws  its  moon  in  a  given  time  with  the  distance 
the  sun  draws  the  planet  in  the  same  tinxe.  The  weight 
of  a  planet  without  a  moon  can  be  found  by  comparing  its 
disturbance  of  another  planet's  motion  with  the  disturb- 
ance of  the  same  planet's  motion  by  a  planet  whose  weight 
is  known. 


266  ASTRONOMY. 


CONCLUSION. 

WE  have  now  become  somewhat  acquainted  with  the 
heavenly  bodies,  and  with  the  force  by  which  they  act 
upon  one  another. 

Our  attention  was  first  called  to  the  motions  of  these 
bodies,  and  we  find  that  they  are  all  describing  accurate 
circles  about  the  earth  from  east  to  west  once  in  twenty- 
four  hours.  An  examination  of  the  vibration  of  a  free  pen- 
dulum taught  us,  however,  that  the  earth  is  rotating  from 
west  to  east,  and  that  the  motion  we  had  first  observed  is 
only  apparent.  We  soon,  however,  discovered  that  certain 
of  these  bodies  are  moving  eastward  among  the  stars  with 
considerable  rapidity,  and  usually  in  very  irregular  paths. 
We  noticed  the  rude  and  complex  systems  by  which  the 
ancients  attempted  to  account  for  these  motions,  and  were 
taught  by  Kepler  that  these  bodies,  together  with  the 
earth,  form  a  group  by  themselves,  and  that  they  all,  ex- 
cept the  moon,  revolve  in  ellipses  about  the  sun.  These 
bodies  are  the  planets. 

We  next  inquired  how  long  it  takes  each  of  these  bodies 
to  complete  a  revolution  about  the  sun,  and  the  simple 
observation  of  the  interval  between  two  successive  con- 
junctions of  the  sun  with  the  same  fixed  star,  and  with 
each  of  the  planets,  enabled  us  to  answer  this  inquiry. 

'  We  next  sought  the  relative  distances  of  the  planets  from 
the  sun,  and  were  enabled  to  find  these  distances  by  simply 
observing  the  greatest  elongation  of  the  inferior  planets 
and  the  retrogression  of  the  superior  planets  during  one 
day  when  they  are  in  opposition.  We  then  found  the  ac- 
tual distance  of  the  earth  from  the  sun  simply  by  observ- 
ing a  transit  of  Venus,  and  by  measuring  a  short  distance 
upon  the  earth. 

We  next  directed  our  attention  to  the  moon,  and  saw 


ASTRONOMY.  267 

that  her  motion  could  be  explained  only  on  the  supposi- 
tion that  she  revolves  about  the  earth  in  an  ellipse ;  and 
that  her  distance  from  the  earth's  centre  could  be  found  by 
simply  pointing  a  telescope  at  her  from  the  observatories 
at  Greenwich  and  the  Cape  of  Good  Hope,  and  measuring 
the  inclination  of  these  telescopes  to  each  other. 

Having  learned  so  much  about  the  motions  and  dis- 
tances of  the  moon  and  the  planets,  we  next  inquired  the 
distance  between  our  earth  and  the  stars.  We  found  that 
in  some  cases  the  telescope  does  not  have  quite  the  same 
direction  when  pointed  at  a  fixed  star  from  opposite  points 
in  the  earth's  orbit,  and  that  we  can  measure  this  differ- 
ence of  direction,  and  thus  ascertain  the  distance  of  the 
stars  from  the  earth.  This  inquiry  led  us  to  the  unex- 
pected conclusion  that  our  sidereal  system  is  so  vast,  that, 
were  all  the  stars  which  compose  it  suddenly  destroyed,  it 
would  be  some  four  years  before  light,  travelling  with  the 
velocity  of  190,000  miles  a  second,  could  inform  us  of  the 
destruction  of  the  nearest,  and  several  thousand  years  be- 
fore it  could  inform  us  of  the  destruction  of  the  most 
remote.  And  at  the  same  time  we  caught  sight  of  outly- 
ing sidereal  systems,  which  probably  are  not  inferior -in 
magnitude  to  our  own,  but  which  even  with  the  aid  of  a 
telescope  appear  only  as  minute  patches  of  hazy  light. 

Since  our  sun  at  the  distance  of  the  fixed  stars  would 
shine  only  as  a  star  of  the  second  magnitude,  we  saw  that 
all  the  stars  are  suns ;  and  a  more  careful  examination  of 
these  bodies  taught  us  that  they  appear  fixed  only  because 
they  are  separated  from  us  by  such  immense  distances. 
We  found  that  our  sun  is  moving  toward  a  point  in  the 
constellation  Hercules  ;  that  many  of  the  stars  have  prop- 
er motions  ;  and  that  Arcturus  and  other  stars  are  really 
moving  through  space  with  a  velocity  about  six  hundred 
times  that  of  a  cannon-ball. 

We  thus  learned  that  our  sun,  moons,  and  planets  prob- 


263  ASTRONOMY. 

ably  form  but  one  of  millions  of  such  groups,  and  that 
while  in  each  of  these  groups  the  moons  are  revolving 
about  the  planets  and  the  planets  about  the  suns,  the 
suns  themselves  are  revolving  about  one  another  in  sys- 
tems more  or  less  complicated. 

After  having  thus  learned  the  motions  and  distances  of 
the  members  of  our  solar  system,  and  the  motions  and  dis- 
tances of  a  few  of  the  stars,  we  next  inquired  what  is  known 
of  the  physical  features  of  each  of  these  bodies.  On  this 
point  we  found  our  knowledge  to  be  extremely  limited. 
The  telescope  has  revealed  to  us  that  there  are  rocks, 
mountains,  and  volcanic  craters  upon  the  surface  of  the 
moon,  and  we  think  that  Mercury,  Venus,  and  Mars  re- 
semble the  earth  and  moon  in  this  respect.  We  know 
that  the  earth  and, Mars  rotate  on  their  axes  in  about 
twenty-four  hours,  and  we  think  that  Mercury  and  Venus 
rotate  in  the  same  time.  We  know  that  each  one  of  these 
planets  has  an  atmosphere.  We  know  nothing  of  the 
physical  constitution  of  the  minor  planets.  And  of  the 
outer  planets,  we  know  only  that  Jupiter  and  Saturn  rotate 
on  their  axes  in  about  ten  hours,  and  that  Jupiter  is  at- 
tended by  four  moons,  and  Saturn  by  eight  moons  and  a 
complex  system  of  rings.  Of  Uranus  and  Neptune  we 
know  only  that  they  are  attended  by  a  few  moons,  whose 
motions  are  retrograde.  We  know  that  the  sun  rotates  on 
his  axis  in  about  twenty-five  days,  that  he  has  an  atmos- 
phere several  thousand  miles  deep,  and  that  there  are  dark 
spots  on  his  disc. 

We  think  that  in  the  atmosphere  of  the  sun  the  vapors 
of  such  substances  as  iron,  which  pass  from  the  gaseous 
to  the  liquid  state  at  a  temperature  above  a  white  heat, 
condense  into  a  cloudy  stratum,  giving  rise  to  the  solar 
photosphere,  and  that  these  clouds  are  sometimes  cooled 
by  downward  and  sometimes  lifted  into  ridges  by  up- 
ward currents,  and  that  this  is  the  cause  of  the  spots  and 
faculx. 


ASTRONOMY.  269 

We  next  learned  that  a  moving  body  when  left  to  itself 
will  always  move  in  a  straight  line  and  with  uniform  ve- 
locity. 

A  further  study  of  the  paths  of  bodies  falling  to  the 
earth,  and  of  those  of  the  heavenly  bodies,  taught  us  that 
these  bodies  are  all  acted  upon  by  a  force  which  tends  to 
draw  them  together,  and  whose  intensity  varies  directly  as 
the  mass  of  the  bodies  acted  upon  and  inversely  as  their 
distance  from  one  another ;  and  that  this  force  is  the 
same  as  that  which  draws  a  stone  to  the  earth. 

We  have  found  that  the  action  of  this  force  is  so  well 
understood  that  we  can  explain  by  it  not  only  the  general 
form  of  the  paths  described  by  the  heavenly  bodies,  but  the 
many  and  complicated  disturbances  which  the  planets 
cause  in  one  another's  motions  ;  that  we  are  able  to  pre- 
dict disturbances  whose  existence  had  not  been  revealed 
by  observation,  and  by  the  study  of  perturbations  already 
observed  to  point  out  the  position  of  planets  before  un- 
known. 

We  have  fo'undy  too,  that  the  knowledge  of  the  force 
which  acts  among  the  heavenly  bodies  and  through  planet- 
ary distances  is  of  no  less  practical  value  than  the  knowl- 
edge of  the  forces  of  affinity  and  electricity  which  act 
among  the  atoms  and  molecules  of  matter  and  through 
atomic  and  molecular  spaces.  For  it  is  only  by  a  correct 
knowledge  of  the  action  of  this  force  that  astronomers  be- 
come acquainted  with  all  the  irregularities  of  the  moon's 
motion,  and  are  enabled  to  construct  tables  by  which 
navigators  at  sea  can  read  longitude  from  the  heavens 
with  accuracy. 

We  have  thus  seen  that  the  groupings  and  movements 
of  the  heavenly  bodies  result  from  a  single  force  acting 
among  them ;  and  that,  by  a  study  of  these  groupings  and 
movements,  we  have  arrived  at  a  complete  knowledge  of 
the  law  by  which  this  force  acts. 


270  ASTRONOMY. 

In  another  part  of  this  Course  we  have  seen  that  bodies 
are  made  up  of  atoms  which  are  grouped  into  molecules 
and  into  masses.  Are  these  atoms  also  in  motion,  and  are 
their  groupings  and  movements  regulated  by  a  single  force 
acting  among  them  ;  and  are  electricity,  light,  and  heat 
only  disturbances  of  these  atomic  and  molecular  move- 
ments ?  The  achievements  of  astronomy  lead  us  to  hope 
that  we  may  at  a  future  day  be  able  to  measure  the  minute 
distances  between  the  atoms,  and  to  discover  in  what  paths 
they  move  and  the  laws  by  which  the  force  acting  among 
them  is  governed. 


IV. 

ORIGIN,     TRANSMUTATION,     AND 
CONSERVATION  OF  ENERGY. 


ORIGIN,     TRANSMUTATION,     AND     CON- 
SERVATION   OF    ENERGY. 


215.  Actual  and  Potential  Energy.  —  A  weight  at  rest  on 
the  ground  cannot  move,  or  do  work  of  any  kind.     It  is 
therefore  said  to  have  no  energy,  or  ability  to  do  work.     If 
the  same  weight  is  raised  from  the  ground  and  suspended, 
it  still  manifests  no  energy ;  that  is,  so  long  as  it  remains 
suspended  it  can  do  no  work.     The  moment  it  is  released, 
however,  it  begins  to  fall,  and  in  falling  can  drive  a  clock, 
or  do  other  work.    While,  then,  a  weight  rests  on  the  earth, 
it  has  no  energy,  and  it  is  not  possible  for  it  to  manifest 
any.     When  the  weight  is  raised  from  the  earth,  it  may  not 
manifest  any  energy,  but  it  is  always  possible  for  it  to  do 
so.     In  this  case  it  is  said  to  have  a  possible  or  potential 
energy.     When  the  weight  is  falling  it  has  an  actual  or  dy- 
namical energy.     Every  moving  body,  then,  has  a  dynami- 
cal energy ;  and  every  body  which  is  so  situated  that  it  can 
be  moved  by  gravity  has  a  potential  energy. 

216.  Mechanical,   Molecular,   and  Muscular  Energy. — 
When,  as  in  the  case  of  the  falling  weight,  th'e  motion  of  a 
body  is  visible,  «its  energy  is  called  mechanical.     But  we 
have  seen  that  heat  can  separate  and  rearrange  the  mole- 
cules of  a  body,  and,  in  so  doing,  it  does  work.     Again, 
light  can  effect  chemical  changes ;  and  electricity  in  motion 
can  turn  a  magnetic  needle,  or  make  a  magnet.     The  mo- 
tions which  manifest  themselves  as  heat,  light,  and  elec- 
tricity are  invisible.     They  are  not  movements  of  a  body 

12*  R 


274  CONSERVATION    OF    ENERGY. 

as  a  whole,  but  of  its  molecules  among  themselves.     The 
energy  of  these  movements  is  called  molecular. 

The  movements  of  bodies  which  manifest  themselves  as 
sound  are  either  visible,  or  can  be  easily  made  so.  The 
energy  of  these  movements,  then,  is  to  be  regarded  as 
mechanical  rather  than  as  molecular. 

The  energy  manifested  in  the  bodies  of  animals  is  called 
.muscular  energy. 

There  are,  then,  three  kinds  of  dynamical  energy,  — 
rthat  manifested  in  ordinary  motion  and  in  a  sounding 
.body,  called  mechanical  energy  ;  that  manifested  in  the 
molecular  movements  of  light,  heat,  and  electricity,  called 
molecidar  energy ;  and  that  manifested  in  the  bodies  of 
animals,  called  muscular  energy. 

It  must  be  understood,  however,  that  these  kinds  of 
energy  do  not  differ  in  themselves,  but  only  in  the  way  in 
.which  they  are  manifested. 

217.  Affinity,  Cohesion,  and  Gravity  are  the  Forces  which 
tend  to  convert  Potential  into  Dynamical  Energy.  —  We  have 
seen  that  a  weight  raised  from  the  earth  has  a  potential 
energy,  which  gravity  tends  to  convert  into  dynamical 
energy.  When  the  molecules  of  a  body  are  separated  by 
melting  and  boiling,  cohesion  tends  to  draw  them  together 
again,  and  thus  to  convert  their  potential  into  dynamical 
energy,  which  appears  as  heat  Again,  when  the  elements 
of  a  compound  are  separated,  they  have  a  potential  energy, 
since  it  is  possible  for  them  to  unite  again.  The  force 
which  tends  to  draw  them  together,  and  thus  to  convert 
their  potential  into  dynamical  energy,  is  affinity. 

When,  therefore,  the  atoms  of  different  elements  are 
separated,  they  have  a  potential  energy,  which  affinity 
tends  to  convert  into  dynamical  energy.  When  the  mole- 
cules of  a  body  are  separated,  they  have  a  potential  energy, 
which  cohesion  tends  to  convert  into  dynamical  energy. 
When  bodies  are  separated,  they  have  a  potential  en- 


CONSERVATION    OF    ENERGY.  275 

ergy,  which  gravity  tends  to  convert  into  dynamical 
energy.  The  first  two  forces  act  through  insensible  dis- 
tances, and  give  rise  to  molecular  energy ;  the  last  acts 
through  all  distances,  and  gives  rise  to  mechanical  energy.* 

218.  Mechanical  Energy  may  be  converted  into  Heat. — 
We  have  a  familiar  illustration  of  this  in  the  lighting  of  a 
friction  match.     A  portion  of  the  energy  employed  in  rub- 
bing the  match  is  converted  by  the  friction  into  heat,  which 
ignites  the  phosphorus.     Here  there  is  a  double  transfer 
of  energy.     The  muscular  energy  of  the  arm  is  converted 
into  mechanical  energy  in  the  moving  match,  and  a  part 
of  this  into  heat  by  the  friction. 

Before  matches  were  invented,  the  flint  and  steel  were 
used  for  the  same  purpose.  The  steel  was  struck  against 
the  flint,  and  the  spark  obtained  was  caught  in  tinder.  A 
part  of  the  mechanical  energy  of  the  steel  appeared  as 
heat  in  the  spark. 

Indians  are  said  to  obtain  fire  by  vigorously  rubbing  to- 
gether two  pieces  of  dry  wood.  In  this  case,  too,  the  heat 
is  nothing  but  mechanical  energy  appearing  in  a  new 
form. 

Iron  can  be  heated  red-hot  by  hammering  it.  And, 
generally,  heat  is  developed  by  friction  and  percussion. 

219.  Count  Rumford's  Experiment.  —  Until  recently,  heat 
has  been  regarded  as  a  substance,  or  a  form  of  matter.     It 
was  supposed  that  this  substance  was  taken  up  by  bodies 
much  as  water  is  taken  up  by  a  sponge,  and  in  this  state  it 
\vas  said  to  be  latent ;  but  when  bodies  were  rubbed  or 
struck  together,  a  portion  of  the  heat  was  squeezed  out  of 
them,  and  thus  became  sensible.     The  more  heat  a  body 
could  take  up  and  render  latent,  the  greater  was  said  to  be 
its  capacity  for  heat. 

This  theory  was  first  attacked  by  Count  Rumford,  in 

*  Magnetism,  like  gravity,  tends  to  draw  bodies  together  ;  but  it 
does  not,  like  gravity,  act  upon  all  bodies. 


276  CONSERVATION    OF    ENERGY. 

1798.  While  superintending  the  boring  of  cannon  in  the 
workshops  of  the  Military  Arsenal  at  Munich,  he  was 
struck  by  the  high  temperature  which  the  cannon  acquired 
in  the  process,  and  the  still  more  intense  heat  of  the  metal- 
lic chips  separated  from  it  by  the  borer.  He  was  thus  led 
to  inquire  into  the  source  of  this  heat.  Was  it  squeezed 
out  of  the  chips  ?  If  so,  their  capacity  for  heat  must  be 
reduced  sufficiently  to  account  for  all  the  heat  rendered 
sensible.  He  found,  however,  that  the  chips  had  exactly 
the  same  capacity  for  heat  as  slices  of  the  same  metal  cut 
off  by  a  fine  saw  where  heating  was  avoided.  It  was  evi- 
dent, then,  that  the  heat  could  not  have  been  furnished  at 
the  expense  of  the  metallic  chips. 

Count  Rumford  then  constructed  a  machine  for  the 
express  purpose  of  generating  heat  by  friction.  It  con- 
sisted of  a  metallic  cylinder,  which  was  turned  on  its  axis 
by  horse-power  while  a  blunt  borer  was  forced  against  its 
solid  bottom.  To  measure  the  heat,  a  small  hole  was 
bored  into  the  cylinder,  in  which  was  placed  a  thermome- 
ter. At  the  beginning  of  the  experiment  the  temperature 
of  the  cylinder  was  60°.  At  the  end  of  30  minutes,  or 
after  the  cylinder  had  made  960  revolutions,  the  tempera- 
ture had  risen  to  130°.  He  now  removed  the  dust  which 
the  borer  had  detached  from  the  bottom  of  the  cylinder, 
and  found  it  to  weigh  only  837  grains,  or  less  than  two 
ounces.  "  Is  it  possible,"  he  exclaimed,  "  that  the  very 
considerable  quantity  of  heat  produced  in  this  experiment 
—  a  quantity  which  actually  raised  the  temperature  of  113 
pounds  of  gun-metal  at  least.  70°  Fahrenheit  —  could  have 
been  furnished  by  so  inconsiderable  a  quantity  of  metallic 
dust,  and  this  merely  in  consequence  of  a  change  in  its 
capacity  for  heat  ? "  But  he  found  by  careful  experiment 
that  the  capacity  of  the  metal  for  heat  was  changed  very 
slightly,  if  at  all,  by  the  boring.  He  concluded,  therefore, 
that  heat  could  not  be  a  material  substance,  but  was  merely 


CONSERVATION    OF    ENERGY.  277 

a  mode  of  motion.  The  mechanical  motion  of  the  borer 
had  been  converted  into  molecular  motion,  and  appeared 
as  heat. 

220.  Sir  Humphrey  Davy 's  Experiment. —  Sir  Humphrey 
Davy  proved  that  heat  is  not  material,  by  an  experiment 
even  more  conclusive  than  Count  Rumford's. 

We  have  already  seen  that  a  large  amount  of  heat  is 
rendered  latent  in  converting  ice  into  water.  A  pound  of 
water,  therefore,  contains  considerably  more  heat  than  a 
pound  of  ice  ;  and,  of  course,  it  would  be  impossible  to 
melt  ice  by  the  heat  squeezed  out  of  it.  But  Sir  Hum- 
phrey Davy  found  that  he  could  melt  ice  by  rubbing  two 
pieces  of  it  together.  If,  then,  heat  is  material,  the  fric- 
tion must  have  induced  some  change  in  the  pieces  of  ice 
which  enabled  them  to  attract  heat  from  the  bodies  with 
which  they  were  in  contact.  He  next,  by  means  of  clock- 
work, caused  two  pieces  of  ice  to  rub  together  in  an  ex- 
hausted receiver,  and  they  melted  as  before,  showing  that 
the  heat  could  not  have  been  taken  from  the  air.  It 
might,  however,  have  been  conducted  to  the  ice  through 
the  pump-plate  and  the  clock-work.  He  next  placed  a 
piece  of  ice  upon  the  pump-plate,  and  set  the  clock-work 
upon  that ;  and  the  ice  was  again  melted  by  the  friction. 
If  the  heat  had  been  drawn  up  through  the  ice,  the  ice 
would  have  been  colder  at  the  top  than  at  the  bottom. 
But  he  had  cut  a  groove  in  the  upper  face  of  the  ice,  and 
had  filled  it  with  water.  As  the  temperature  of  the  ice 
was  32°,  this  water  would  have  frozen  had  the  temperature 
of  this  surface  fallen  ;  but  the  water  did  not  freeze.  It 
was  evident,  then,  that  the  heat  could  not  have  come  up 
through  the  pump-plate.  It  might  still  be  objected  that 
the  heat  could  have  come  by  radiation  from  the  receiver ; 
but  the  receiver  was  kept  colder  than  the  ice,  and  hence 
must  have  radiated  less  heat  to  the  ice  than  the  ice  radi- 
ated back  again. 


278  CONSERVATION    OF    ENERGY. 

If,  then,  heat  is  matter,  we  are  driven  to  the  conclusion 
that  this  matter  must  have  been  created  by  the  friction. 
Now,  we  know  that  in  the  friction  mechanical  energy  dis- 
appeared, while  heat  was  produced.  The  only  rational 
inference,  then,  seems  to  be,  that  the  mechanical  energy 
was  transformed  into  heat ;  in  other  words,  that  the  me- 
chanical motion  of  the  ice  was  converted  into  the  molecu- 
lar motion  of  heat. 

221.  All  Mechanical  Energy  is  ultimately  converted  into 
Heat.  —  When  a  falling  body  strikes  the  earth,  it  becomes 
heated.     In  this  case  the  whole  energy  of  the  body  is  con- 
verted into  heat.     When  bodies  are  rubbed  together,  their 
energy,  as  we  have  seen,  is  converted  into  heat. 

The  energy  of  a  running  stream  is  gradually  converted 
into  heat  by  the  friction  against  its  banks  and  bed  and 
among  its  particles.  If  it  is  made  to  turn  the  wheels  of  a 
factory  on  its  way,  the  rubbing  of  the  parts  of  the  ma- 
chinery against  each  other  and  against  the  air,  together 
with  the  various  kinds  of  work  done  by  the  machinery, 
converts  the  mechanical  energy  of  the  water-wheel  into 
heat. 

A  railway  train  is  really  stopped  by  the  conversion  of  its 
motion  into  heat.  When  this  has  to  be  done  quickly,  the 
change  is  hastened  by  increasing  the  friction  by  means  of 
the  brakes.  On  the  other  hand,  in  order  to  prevent  the 
loss  of  energy  while  the  train  is  in  motion,  the  axles  of 
the  wheels  are  kept  carefully  oiled,  that  they  may  turn 
with  as  little  friction  as  possible. 

When  unlike  substances  are  rubbed  together,  a  part  of 
the  energy  is  first  converted  into  electricity,  but  ultimately 
into  heat. 

222.  When  Mechanical  Energy  is  converted  into  Heat,  the 
same  Amount  of  Energy    always  gives   rise  to   the  same 
Amount  of  Heat.  —  This  was  first  shown   by  Joule,  who 
began  his  experiments  in    1843   and  continued  them  till 


CONSERVATION    OF    ENERGY. 


279 


1849.  He  converted  mechanical  energy  into  heat  by 
means  of  friction.  He  first  examined  cases  of  the  friction 
of  solids  against  liquids.  The  apparatus  used  for  this  pur- 
pose is  shown  in  Figure  101.  B  is  a  cylindrical  box  hold- 


Fig.  101. 


ing  the  liquid.  In  the  centre  of  the  box  is  an  upright  axis, 
to  which  are  attached  eight  paddles  like  the  one  shown  in 
the  figure.  These  revolve  between  four  stationary  vanes, 
which  prevent  the  liquid  from  being  carried  round.  The 
paddles  are  turned  by  means  of  the  cord  r  and  the  weight 
W.  The  size  of  the  weight  is  such  that  it  descends  with- 
out acquiring  any  velocity,  and  hence  all  its  energy  is 
expended  in  the  friction  of  the  paddles.'  The  degree  to 
which  the  liquid  became  heated  by  the  friction  was  shown 
by  a  thermometer  at  /.  Knowing  the  weight  of  the  liquid, 
its  specific  heat,  and  the  rise  of  temperature  during  the 
experiment,  the  amount  of  heat  generated  could  be  readily 
calculated. 

With  this  machine  Joule  found  that,  whatever  the  liquid 
he  used,  a  weight  of  one  pound  falling  through  772  feet, 


280  CONSERVATION    OI-'    ENERGY. 

or  772  pounds  falling  one  foot,  generated  heat  enough  to 
raise  one  pound  of  water  one  degree  Fahrenheit  in  tem- 
perature, or  one  unit  #f  heat,  as  it  is  called. 

He  also  found  that,  when  solids  were  rubbed  together  by 
the  action  of  a  falling  weight,  one  pound  falling  through 
772  feet  generated  a  unit  of  heat.  In  this  experiment  iron 
discs  were  made  to  rotate  together,  one  against  the  other, 
in  a  vessel  of  mercury. 

If  a  metallic  disc  be  put  into  rapid  rotation  and  then 
brought  between  the  poles  of  a  powerful  electro-magnet,  it 
soon  comes  to  rest..  It  will  now  be  found  very  difficult  to 
turn  it,  and  that  it  becomes  heated  as  it  rotates.  Joule 
found  in  this  case,  as  in  the  others,  that,  if  the  disc  were 
turned  by  a  falling  weight,  one  pound  descending  772  feet 
generated  a  unit  of  heat. 

The  force  necessary  to  raise  one  pound  one  foot  is 
called  a  foot-pound ;  and  this  is  the  same  force  which  a 
pound  acquires  in  falling  one  foot  from  a  state  of  rest. 

We  see,  then,  that  when  mechanical  energy  is  converted 
into  heat,  the  same  amount  of  energy  always  gives  rise  to 
the  same  amount  of  heat,  and  that  772  foot-pounds  of 
mechanical  force  are  equivalent  to  one  unit  of  heat.  For 
this  reason,  we  call  772  foot-pounds  the  mechanical  equiva- 
lent of  heat. 

223.  Heat  may  be  converted  into  Mechanical  Energy.  — 
The  steam-engine  is  a  contrivance  for  converting  heat  into 
mechanical  energy.  The  heat  converts  the  water  into 
steam,  and  gives  to  this  steam  an  expansive  force  ;  and 
this  expansive  force  is  made  to  move  a  piston  by  means  of 
the  arrangement  shown  in  Figure  102.  The  steam  coming 
from  the  boiler  by  the  tube  x  passes  into  the  box  d.  From 
this  box  run  two  pipes,  tf.and  b,  for  carrying  the  steam, 
one  above  and  the  other  below  the  piston.  A  sliding- 
valve  y  is  so  arranged  that  it  always  closes  one  of  these 
pipes.  In  the  right-hand  figure,  the  lower  pipe  b  is  open, 


CONSERVATION    OF    ENERGY. 


28l 


and  the  steam  can  pass  in  under  the  piston  and  force  it  up. 
At  the  same  time,  the  steam  which  has  done  its  work  on 
the  other  side  of  the  piston  passes  out  through  the  pipes  a 

Fig.  102. 


and  O.  The  sliding-valve  is  connected  by  means  of  the 
rod  i  with  the  crank  of  the  engine,  so  that  it  moves  up  and 
down  as  the  piston  moves  down  and  up.  As  soon,  then, 
as  the  piston  has  reached  the  top  of 'the  cylinder,  the 
sliding-valve  is  brought  into  the  position  shown  in  the  left- 
hand  figure.  The  steam  now  passes  into  the  cylinder 
above  the  piston  by  the  pipe  a  and  forces  the  piston  down, 
while  the  steam  on  the  other  side  which  has  done  its  work 
goes  out  through  b  and  O.  The  sliding-valve  is  now  in 
the  position  shown  in  the  right-hand  figure,  and  the  piston 
is  driven  up  again  as  before  ;  and  thus  it  keeps  on  moving 


282  CONSERVATION   OF    ENERGY. 

up  and  down,  or  in  and  out.     By  means  of  a  crank  it  can 
be  made  to  drive  machinery. 

224.   The  same  Amount  of  Heat  always  gives  rise  to  the 

same  Amount  of  Mechanical  Energy.  —  In  Figure  103,  C  is 

a  box  a  foot  square.     Suppose  a  a  to  be  a 

Fig.  103. 

partition  one  foot  from  the  bottom,  so  as  to 
shut  in  a  cubic  foot  of  air.  Suppose  this 
partition  to  be  immovable,  and  the  air  be- 
neath to  be  heated.  Its  elastic  force  will 
be  increased,  but  it  cannot  expand.  We 
will  next  suppose  that  a  a  is  movable,  but 
without  weight,  and  that  the  air  beneath  is 
heated  as  before.  On  raising  its  tempera- 
ture 490°  its  volume  will  be  doubled,  and 
a  a  will  of  course  be  raised  one  foot  to  b  b.  In  raising 
a  a  one  foot  it  has  had  to  raise  the  air  above  it.  Now, 
this  air  presses  15  pounds  upon  every  square  inch,  and 
15  X  144  =  2,160  pounds  upon  the  whole  surface.  From 
the  specific  heat  of  air,  we  know  that  to  raise  a  cubic 
foot  of  air  490°,  when  it  is  free  to  expand,  9.5  units  of 
heat  are  required. 

But  we  have  seen  that  a  part  of  the  heat  which  enters  a 
body  is  used  in  expanding  it,  and  a  part  in  raising  its  tem- 
perature. In  the  above  experiment,  how  much  heat  is 
used  in  raising  the  temperature  ?  This  is  equivalent  to 
asking  how  much  heat  is  required  to  raise  the  cubic  foot 
of  air  490°  when  it  is  not  allowed  to  expand.  We  have 
learned  that  the  computed  velocity  of  sound  in  air  is  less 
than  its  observed  velocity,  and  that  this  is  owing  to  the 
heat  developed  in  the  compressed  portion  of  the  sound- 
wave. From  the  ratio  which  exists  between  the  observed 
and  the  computed  velocity,  it  is  found  that  the  specific  heat 
of  air  when  free  to  expand  must  be  1.42  of  its  heat  when 
not  allowed  to  expand.  Hence  the  heat  required  to  raise 
the  temperature  of  the  cubic  foot  of  air  490°,  when  it  is 


CONSERVATION    OF    ENERGY. 


283 


not  allowed  to  expand,  is  found  by  the  following  proportion 
to  be  6.7  units  :  — 

1.42  :  i  =  9.5  :  6.7. 

The  amount  of  heat,  then,  used  in  expanding  the  air  — • 
that  is,  in  raising  2,160  pounds  one  foot  high  —  is  2.8 
units.  Dividing  2,160  by  2.8,  we  get  772,  nearly. 

Since  there  is  no  cohesion  among  the  particles  of  air, 
the  whole  expansive  force  is  used  in  raising  the  weight. 

There  is  a  prevalent  impression  that  the  expanding  of 
air  is  in  itself  a  cooling  process  (that  is,  consumes  heat) ; 
but  this  is  not  the  case,  unless  the  air  in  expanding  per- 
forms work.  This  was  proved  by  Joule  in  the  following 
manner.  In  Figure  104  we 
have  two  strong  vessels,  of  Fis- 104- 

which  A  contains  air  com- 
pressed under  a  pressure  of 
some  20  atmospheres,  while 
in  B  is  a  vacuum.  The  two 
are  connected  by  a  tube  with 
a  stop-cock.  The  whole  ap- 
paratus is  placed  in  a  vessel 
of  water.  After  the  tempera- 
ture of  the  water  has  been 
very  carefully  ascertained, 

open  the  stop-cock  and  allow  the  air  to  expand.  The 
temperature  of  the  water  remains  unchanged.  As  there  is 
no  resistance  to  the  expansion  of  the  air,  no  heat  is  con- 
sumed in  the  expansion. 

We  see,  then,  that  772  foot-pounds  of  mechanical  force 
are  equivalent  to  a  unit  of  heat,  and  that  a  unit  of  heat  is 
equivalent  to  772  foot-pounds  of  mechanical  force. 

225.  The  Molecular  Energy  produced  by  Cohesion  is  con- 
verted into  Heat.  —  We  have  seen  that  the  heat  which 
enters  a  body  is  employed  in  three  ways,  —  in  raising  the 


284  CONSERVATION   OF    ENERGY. 

temperature  of  the  body,  in  expanding  it,  and  in  changing 
its  state.  A  body  is  expanded  by  the  separation  of  its 
molecules  ;  and  its  state  is  changed  either  by  the  separa- 
tion or  the  rearrangement  of  its  molecules.  A  part  of  the 
heat,  then,  which  enters  a  body  performs  work  ;  and,  as 
this  work  is  done  within  the  body,  it  is  called  interior  work. 
We  have  already  noticed  that,  when  it  does  this  interior 
work,  it  gives  to  the  molecules  potential  energy ;  and  that, 
when  these  molecules  are  brought  together  again  by  cohe- 
sion, the  potential  energy  appears  as  heat.  The  enormous 
strength  of  the  cohesive  force  is  shown  by  the  amount  of 
heat  which  it  requires  to  melt  ice,  or  to  convert  water  into 
steam.  We  have  seen  that  merely  to  melt  a  pound  of  ice 
at  a  temperature  of  32°  Fahrenheit  requires  143  units  of 
heat,  which  is  equivalent  to  the  force  required  to  lift 
10,396  pounds,  or  about  55  tons,  a  foot  high.  And  to 
convert  a  pound  of  boiling  water  into  steam  requires  967 
units  of  heat,  equivalent  to  the  force  required  to  lift 
746,524  pounds,  or  about  373  tons,  a  foot  high.  The 
force  of  gravity  is  almost  as  nothing  compared  with  this 
molecular  force. 

226.  The  Molecular  Energy  of  Affinity  is  sometimes  con- 
verted into  Electricity.  —  We   have   seen   that,   in  all  the 
forms  of  voltaic  battery,  electricity  is  generated  by  chemi- 
cal action.     Here  the  energy  of  affinity  is  converted  into 
electricity.     The  same  amount  of  chemical  action  always 
gives  rise  to  the  same  amount  of  electricity. 

227.  The  Energy  of  Affinity  always  gives  rise  to  Heat.  — 
Every  form  of  chemical  combination  develops  heat,  which 
is  nothing  but  the  energy  of  affinity  reappearing  in  a  new 
form.     The  strength  of  affinity  is  shown  by  the  amount  of 
heat    developed    when   oxygen   combines   with   hydrogen. 
The  heat  thus  generated  can  be  found  by  the  apparatus 
shown  in  Figure    105.     Two  measures  of  hydrogen   and 
one  of  oxygen  are  put  into  the  strong  copper  vessel  #,  and 


CONSERVATION    OF    ENERGY.  285 

this  vessel  is  put  into  a  larger  one  filled  with  water.  This 
in  turn  is  suspended  in  a  cylinder  with  a  movable  cover  at 
each  end,  and  the  whole  is  enclosed  in  a  fourth  cylindrical 
vessel,  which  may  be  rotated  on  a  horizontal  axis.  The 

Fig.  105. 


apparatus  is  first  rotated  for  some  time,  in  order  to  bring 
all  its  parts  to  the  same  temperature,  which  is  measured  by 
a  very  delicate  thermometer.  The  electric  current  is  sent 
through  the  vessel  a,  where  it  heats  a  fine  platinum  wire 
red-hot,  and  explodes  the  mixed  gases.  The  apparatus  is 
again  rotated  about  half  a  minute  to  make*  the  temperature 
uniform  throughout,  and  the  temperature  is  again  measured 
by  the  thermometer.  The  rise  of  temperature  shows  the 
amount  of  heat  generated  by  the  combination  of  the  gases. 
It  is  found  in  this  way  that,  when  the  oxygen  combines 
with  one  pound  of  hydrogen,  61,000  units  of  heat  are  gen- 
erated. Hence  the  force  which  has  combined  the  two 
gases  is  equal  to  61,000  X  772  =  47,092,000  foot-poundSj 


286 


CONSERVATION    OF    ENERGY. 


or  the  force  necessary  to  raise  23,546  tons  a  foot  high,  or 
to  throw  one  ton  to  a  height  of  more  than  four  miles. 

We  see,  then,  that  the  force  even  of  cohesion  is  insignifi- 
cant compared  with  that  of  affinity. 

By  a  modification  of  the  apparatus  described  above,  it 
is  found  that  a  pound  of  carbon,  in  combining  with  oxy- 
gen, gives  out  about  14,500  units  of  heat,  equivalent  to 
11,194,000  foot-pounds. 

228.  The  Energy  of  Affinity  sometimes  reappears  as  Mus- 
cular Force.  —  The  body  is  continually  wasting  away.    The 
waste  is  supplied  by  the  food  we  eat.     The  waste  products 
of  the  body  are  burned-up  food,  —  that  is,  the  elements  of 
the  food  combined  with  oxygen.     The  energy  of  this  com- 
bination reappears  as  heat  and  muscular  force.     The  ma- 
terials of  the  body,  as  we  have  seen,  are  either  tertiary 
(compounds   of  oxygen,   hydrogen,    and   carbon)   or  qua- 
ternary   (compounds    of   oxygen,    hydrogen,    carbon,   and 
nitrogen).     It  has  been  found  that  the  muscular  energy  is 
mainly  due  to  the  combustion  of  the  former. 

We  have  now  seen  that  the  energy  of  affinity  may  be  con- 
verted into  electricity,  heat,  and  muscular  force.  Through 
any  one  of  these  it  may  be  converted  into  mechanical 
force.  The  electricity,  for  instance,  may  be  made  to  de- 
velop magnetism,  and  thus  to  drive  an  electro-magnetic 
engine  ;  the  heat  may  be  made  to  work  a  steam-engine  • 
and  the  muscular  energy  may  be  employed  in  moving  the 
body,  or  in  any  form  of  manual  labor. 

It  is  mainly  the  affinity  of  oxygen  which  develops  these 
different  forms  of  energy.  In  ordinary  combustion  and 
respiration,  the  substance  with  which  the  oxygen  unites  is 
mainly  carbon. 

229.  Energy  may  be  transmuted,  but  not  destroyed.  —  We 
have  now  seen  that  the  mechanical  energy  of  motion,  as 
well  as  that  of  affinity,  may  be  converted  into  heat,  light, 
and  electricity.     Heat  and  light  are  only  different  mani- 


CONSERVATION    OF    ENERGY.  287 

festations  of  the  same  agent ;  and  heat  and  electricity  are 
mutually  convertible.  The  energy  of  affinity  may  also  be 
converted  into  muscular  energy.  Heat  is  the  form  of 
energy  into  which  all  the  other  forms  of  energy  seem  des- 
tined ultimately  to  be  converted.  In  all  these  transforma- 
tions no  energy  is  lost.  The  heat  which  finally  results 
from  them  may  either  be  radiated  into  space  (where  it  may 
become  insensible  on  account  of  its  extreme  diffusion),  or 
else  it  may  be  made  to  separate  atoms,  molecules,  and 
masses,  and  thus  to  confer  potential  energy  upon  them. 
When  these  are  drawn  together  again  by  affinity,  cohesion, 
and  gravity,  they  develop  the  same  amount  of  energy  which 
was  consumed  in  separating  them. 

Energy,  like  matter,  may  assume  a  great  variety  of 
forms  ;  but,  like  matter,  it  is  wholly  indestructible. 

230.  Source  of  Energy.  —  If  left  to  itself,  affinity  would 
soon  bring  all  dissimilar  atoms  together,  and  lock  them  up 
in  compounds  ;  cohesion  would  bring  all  the  molecules  of 
these  compounds  together,  and  lock  them  up  in  solids  ; 
and  gravity  would  bring  all  these  solids  together,  and  hold 
them  in  its  iron  grasp  ;  while  the  heat  developed  by  these 
forces  would  be  radiated  into  space,  and  our  earth  become 
one  dreary  waste,  void  of  all  signs  of  life  and  activity. 
What,  then,  is  the  source  of  the  energy  which  is  thus 
manifesting  itself  in  Protean  forms  ? 

Let  us  consider,  first,  the  energy  developed  by  gravity. 
This  energy  is  seen  in  the  winds,  the  falling  rain,  and  run- 
ning streams.  The  atmosphere  on  each  side  of  the  equa- 
tor is  an  immense  wheel.  The  side  of  this  wheel  next  the 
equator  is  continually  expanded,  and  thus  made  lighter  by 
the  heat  of  the  sun.  Hence  gravity  pulls  down  the  colder 
and  heavier  side  in  the  polar  regions,  and  thus  the  wheel 
is  made  to  turn  round  and  round.  Were  it  not  for  the 
sun's  heat,  it  would  soon  come  to  rest. 

Again,  the  heat  of  the  sun  evaporates  the  waters  of  the 


288  CONSERVATION   OF    ENERGY. 

ocean,  and  in  their  gaseous  state  they  are  swept  round  with 
the  atmospheric  wheel  till  they  come  to  colder  regions, 
where  they  are  condensed,  and  fall  to  the  earth  as  rain, 
and  flow  to  the  ocean  in  rivers.  It  is  due,  then,  to  the 
heat  which  comes  to  the  earth  in  the  sunbeam,  that  gravity 
can  thus  unceasingly  manifest  its  energy. 

The  energy  of  chemical  affinity  which  is  manifested  in 
heat,  light,  and  muscular  force  is,  as  we  have  seen,  devel- 
oped by  its  action  between  oxygen  and  carbon.  How  are 
these  elements  separated  from  carbonic  acid,  so  that  they 
may  be  reunited  by  affinity  ? 

Place  a  leafy  plant  in  a  glass  vessel,  and  let  a  current  of 
carbonic  acid  stream  over  it  in  the  dark,  and  no  change 
takes  place.  Let  the  same  gas  stream  over  the  plant  in 
the  sunshine,  and  a  part  of  it  will  disappear,  and  be  re- 
placed by  oxygen.  When  acted  upon  by  the  sunbeams, 
leaves  of  plants  remove  carbonic  acid  from  the  air,  sepa- 
rate its  carbon  and  oxygen,  retain  the  former,  and  give  the 
latter  back  to  the  air.  When  plants  are  consumed  by  com- 
bustion in  our  furnaces,  and  by  respiration  in  our  bodies, 
this  oxygen  combines  with  carbon  and  develops  energy, 
which  appears  as  mechanical  force  in  our  engines,  and  as 
muscular  force  in  our  bodies. 

In  the  summer,  when  more  sunshine  than  we  need  is 
poured  upon  the  earth,  a  part  of  it  is  absorbed  by  the 
leaves  of  plants,  and  used  to  decompose  carbonic  acid,  to 
build  up  the  varied  forms  of  vegetable  life.  In  this  way, 
the  forests  and  the  fields  become  vast  storehouses  of  force 
which  has  been  gathered  from  the  sunbeam.  When,  there- 
fore, we  burn  fuel  in  our  stoves  and  food  in  our  bodies,  the 
light,  heat,  and  muscular  force  developed  are  only  the  re- 
appearance in  another  form  of  the  sunbeams  stored  up  in 
plants. 

But  this  process  of  gathering  force  from  the  sunlight 
has  been  going  on  for  ages  ;  and  when  we  burn  anthracite 


CONSERVATION    OF    ENERGY.  289 

or  bituminous  coal,  we  are  merely  releasing  the  sunbeams 
imprisoned  in  plants  which  grew  upon  the  earth  before  it 
became  the  dwelling-place  of  man. 

The  energy  of  affinity,  then,  like  that  of  gravity,  is  noth- 
ing but  transmuted  sunshine. 

The  only  form  of  energy  known  to  us  which  does  not 
come  to  the  earth  in  the  sunbeam  is  that  developed  by 
the  ebb  and  flow  of  the  tidal  wave.  This  wave  is  dragged 
round  the  earth  mainly  by  the  attraction  of  the  moon  ;  and 
it  acts  as  a  brake  upon  the  earth's  rotation,  since  it  is 
drawn  from  east  to  west  while  the  earth  is  turning  from 
west  to  east.  The  energy  of  this  wave,  then,  is  developed 
at  the  expense  of  the  earth's  motion  on  its  axis  ;  and  it 
must  tend  to  retard  this  motion,  though  to  so  slight  a 
degree  that  the  observations  of  thousands  of  years  have 
not  served  to  make  it  appreciable. 

231.  The  Amount  of  Heat  given  out  by  the  Sun.  —  In 
Figure  106  we  have  an  apparatus  for  measuring  the  heat 

Fig.  106. 


2QO  CONSERVATION    OF    ENERGY. 

radiated  to  the  earth  by  the  sun.  At  one  end  of  the  in- 
strument there  is  a  shallow  iron  box,  the  cover  of  which  is 
blackened.  The  box  is  filled  with  mercury,  into  which  a 
delicate  thermometer  is  introduced.  At  the  other  end  of 
the  instrument  is  a  disc  of  the  same  diameter  as  the  box. 
If  the  instrument  be  set  in  such  a  way  that  the  shadow  of 
the  box  just  covers  the  disc,  it  is  evident  that  the  sun's 
rays  will  fall  perpendicularly  upon  the  cover.  In  the  first 
place,  the  instrument,  sheltered  from  the  sun,  is  allowed  to 
radiate  its  heat  into  the  clear  sky  for  five  minutes,  and  its 
loss  of  heat  is  noted.  It  is  then  turned  to  the  sun  for  the 
same  length  of  time,  and  its  gain  of  heat  noted.  It  is 
then  turned  again  toward  the  sky,  and  after  five  minutes  its 
loss  of  heat  is  again  noted.  The  mean  between  this  loss 
and  its  loss  during  the  first  five  minutes  will  be  its  loss 
during  the  five  minutes  it  was  turned  towards  the  sun. 
This  loss  added  to  the  gain  already  observed  will  be  the 
whole  heat  which  it  received  from  the  sun  in  five  minutes. 

Now,  as  one  half  of  the  earth  is  always  turned  towards 
the  sun,  the  amount  of  heat  received  by  the  earth  in  five 
minutes  will  be  as  many  times  greater  than  that  received 
by  the  box  as  the  surface  of  a  great  circle  of  the  earth  is 
greater  than  that  of  the  cover  of  the  box.  Making  allow- 
ance for  the  heat  absorbed  by  the  atmosphere,  it  has  been 
calculated  that  the  amount  received  by  the  earth  during  a 
year  would  be  sufficient  to  melt  a  layer  of  ice  100  feet 
thick  and  covering  the  whole  earth.  But  the  sun  radiates 
heat  into  space  in  every  other  direction  as  well  as  towards 
the  earth ;  and  if  we  conceive  a  hollow  sphere  to  surround 
the  sun  at  the  distance  of  the  earth,  our  planet  would 

cover  only of  its  surface.     Hence  the  sun  ra- 

j    2,300,000,000 

diates  into  space  2,300,000,000  times  as  much  heat  as 
the  earth  receives.  Sir  John  Herschel  has  calculated  that 
if  a  cylinder  of  ice  45  miles  thick  were  darted  into  the  sun 
with  the  velocity  of  light  (190,000  miles  a  second),  it  might 


CONSERVATION   OF    ENERGY.  291 

be  melted  by  the  heat  radiated  by  the  sun,  without  lower- 
ing the  temperature  of  the  sun  itself. 

232.  Source  of  the  Surfs  Heat.  —  What,  then,  is  the 
source  of  this  enormous  amount  of  heat  ? 

It  has  been  supposed  by  some  that  the  materials  of  the 
sun  are  undergoing  combustion,  and  that  this  combustion 
develops  the  light  and  heat  which  it  sends  forth.  There 
are,  however,  no  substances  known  to  us  whose  burning 
would  produce  so  much  heat  for  so  long  a  time  as  we 
know  the  sun  has  been  shining.  Carbon  is  one  of  the 
most  combustible  substances  with  which  we  are  acquaint- 
ed ;  but  if  the  sun,  large  as  he  is,  were  a  mass  of  pure 
carbon,  and  were  burning  at  a  rate  sufficient  to  produce 
the  light  and  heat  that  he  is  giving  out,  he  would  be  utterly 
consumed  in  5,000  years.  It  seems  hardly  possible,  then, 
that  the  solar  light  and  heat  can  be  generated  by  ordinary 
combustion. 

One  of  the  most  satisfactory  theories  of  the  origin  of  the 
solar  heat  is  that  recently  devised  by  a  German  physician, 
Mayer,  and  known  as  the  meteoric  theory. 

We  have  seen  that  a  pound- weight  which  has  fallen 
through  772  feet  will,  when  its  motion  is  arrested,  generate 
a  unit  of  heat.  Now,  we  know  that  a  body  falling  that 
distance  will  acquire  a  velocity  of  about  223  feet  a  second. 
Hence  a  pound  ball  moving  with  a  velocity  of  223  feet 
a  second  will  generate  a  unit  of  heat  when  its  motion  is 
arrested.  We  know,  too,  that  the  velocity  with  which  a 
falling  body  strikes  the  ground  is  in  proportion  to  the 
square  root  of  the  height  from  which  it  falls  ;  that  is,  in 
order  to  double  or  treble  its  velocity,  a  body  must  fall  from 
four  or  nine  times  the  height.  A  pound  ball,  then,  moving 
with  a  velocity  of  twice  223  feet  a  second  will  be  able  to 
generate  4  units  of  heat ;  one  moving  with  thrice  this 
velocity,  9  units  of  heat ;  and  so  on.  When,  therefore, 
we  know  the  weight  of  a  body  and  the  speed  with  which  it 


292  CONSERVATION    OF    ENERGY. 

is  moving,  we  can  easily  calculate  how  much  heat  will  be 
generated  on  stopping  it. 

Were  the  earth's  motion  arrested,  its  elements  would 
melt  with  fervent  heat,  and  most  of  them  would  be  con- 
verted into  vapor.  Were  the  earth  to  fall  into  the  sun,  the 
heat  generated  by  the  shock  would  be  sufficient  to  keep 
up  the  solar  light  and  heat  for  95  years.  We  know  that 
countless  swarms  of  meteoric  bodies  are  revolving  in  rings 
about  the  sun,  and  the  well-known  retardation  of  Encke's 
comet  shows  that  these  bodies  must  be  moving  in  a  resist- 
ing medium.  If  so,  they  must  eventually  be  drawn  into 
the  sun,  and,  from  the  velocity  with  which  they  must  strike, 
it  has  been  shown  that  they  could  fall  in  sufficient  numbers 
to  generate  all  the  light  and  heat  of  the  sun,  without  in- 
creasing his  magnitude  enough  to  be  detected,  since  ac- 
curate measures  of  his  diameter  were  first  made.  This 
theory  of  the  sun's  heat  was  first  published  by  Mayer  in 
1848,  and  was  further  developed  by  Thomson  in  1854. 

The  following  account  of  the  meteoric  theory,  as  devel- 
oped by  Thomson,  is  taken  from  Tyndall :  — 

"  '  In  conclusion,  then,'  writes  Professor  Thomson,  '  the 
source  of  energy  from  which  solar  heat  is  derived  is  un- 
doubtedly meteoric The  principal  source  —  per- 
haps the  sole  appreciable  efficient  source  —  is  in  bodies 
circulating  round  the  sun,  at  present  inside  the  earth's 
orbit,  in  the  sunlight  by  us  called  "  zodiacal  light."  The 
store  of  energy  for  future  sunlight  is  at  present  partly 
dynamical,  —  that  of  the  motions  of  these  bodies  round 
the  sun  ;  and  partly  potential,  —  that  of  their  gravitation 
towards  the  sun.  This  latter  is  gradually  being  spent,  half 
against  the  resisting  medium,  and  half  in  causing  a  con- 
tinuous increase  of  the  former.  Each  meteor  thus  goes 
on  moving  faster  and  faster,  and  getting  nearer  and  nearer 
the  centre,  until  some  time,  very  suddenly,  it  gets  so  much 
entangled  in  the  solar  atmosphere  as  to  begin  to  lose  ve- 


CONSERVATION    OF    ENERGY.  293 

locity.  In  a  few  seconds  more  it  is  at  rest  on  the  sun's 
surface,  and  the  energy  given  up  is  vibrated  across  the 
district  where  it  was  gathered  during  so  many  ages,  ulti- 
mately to  penetrate,  as  light,  the  remotest  regions  of 
space.' 

"  From  the  tables  published  by  Professor  Thomson  I  ex- 
tract the  following  interesting  data,  firstly  with  reference  to 
the  amount  of  heat  equivalent  to  the  rotation  of  the  sun 
and  planets  round  their  axes,  —  the  amount,  that  is,  which 
would  be  generated  supposing  a  brake  applied  at  the  sur- 
faces of  the  sun  and  planets  until  the  motion  of  rotation 
was  entirely  stopped ;  secondly,  with  reference  to  the 
amount  of  heat  due  to  the  sun's  gravitation,  —  the  heat, 
that  is,  which  would  be  developed  by  each  of  the  planets 
in  falling  into  the  sun.  The  quantity  of  heat  is  expressed 
in  terms  of  the  time  during  which  it  would  cover  the  solar 
emission. 

Heat  of  Gravitation,  equal  to  Solar         Heat  of  Rotation,  equal  to  Solar 
Emission  for  a  Period  of  Emission  for  a  Period  of 

Sun 1 16  years      6  days. 

Mercury      .     .    .      6  years  2 14  days  15  " 

Venus    ....     83      "     227     "  99  « 

Earth     ....    94      "     303     "  81  " 

Mars      ....     12      "     252     "  7  " 

Jupiter   .    .     .  32,240      "    .    .    .    .  14     «     144  « 

Saturn    .     .     .    9,650      "    .     .     .     .  2      "     127  u 

Uranus  .    .     .     1,610      "    .    .    .    .  71  " 
Neptune     .     .     1,890      "     .    .     .     . 

"  Thus,  if  the  planet  Mercury  were  to  strike  the  sun,  the 
quantity  of  heat  generated  would  cover  the  solar  emission 
for  nearly  seven  years  ;  while  the  shock  of  Jupiter  would 
cover  the  loss  of  32,240  years.  The  heat  of  rotation  of 
the  sun  and  planets,  taken  together,  would  cover  the  solar 
emission  for  134  years ;  while  the  total  heat  of  gravitation 
(that  produced  by  the  planets  falling  into  the  sun)  would 
cover  the  emission  for  45,589  years. 


294  CONSERVATION    OF    ENERGY. 

"  Whatever  be  the  ultimate  fate  of  the  theory  here 
sketched,  it  is  a  great  thing  to  be  able  to  state  the  condi- 
tions which  certainly  would  produce  a  sun,  —  to  be  able  to 
discern  in  the  force  of  gravity,  acting  upon  dark  matter, 
the  source  from  which  the  starry  heavens  may  have  been 
derived  ;  for,  whether  the  sun  be  produced  and  his  emission 
maintained  by  the  collision  of  cosmical  masses  or  not,  there 
.cannot  be  a  doubt  as  to  the  competence  of  the  cause  as- 
.signed  to  produce  the  effects  ascribed  to  it.  Solar  light  and 
solar  heat  lie  latent  in  the  force  which  pulls  an  apple  to  the 
ground.  The  potential  energy  of  gravitation  was  the  origi- 
nal form  of  all  the  energy  in  the  universe.  As  surely  as  the 
weights  of  a  clock  run  down  to  their  lowest  position,  from 
which  they  can  never  rise  again  unless  fresh  energy  is  com- 
municated to  them  from  some  source  not  yet  exhausted,  so 
surely  must  planet  after  planet  creep  in,  age  by  age,  to- 
wards the  sun.  When  each  comes  within  a  few  hundred 
thousand  miles  of  his  surface,  if  he  is  still  incandescent, 
it  must  be  melted  and  driven  into  vapor  by  radiant  heat. 
Nor,  if  he  be  crusted  over  and  become  dark  and  cool  ex- 
ternally, can  the  doomed  planet  escape  its  fiery  end.  If  it 
'does  not  become  incandescent,  like  a  shooting-star,  by  fric- 
tion in  its  passage  through  his  atmosphere,  its  first-  graze 
on  his  surface  must  produce  a  stupendous  flash  of  light 
and  heat.  It  may  be  at  once,  or  it  may  be  after  two  or 
three  bounds  like  a  cannon-shot  ricochetting  on  a  surface 
of  earth  or  water,  the  whole  mass  must  be  crushed,  melted, 
and  evaporated  by  a  crash,  generating  in  a  moment  some 
thousands  of  times  as  much  heat  as  a  coal  of  the  same 
size  would  produce  by  burning." 

233.  The  Nebular  Hypothesis.  —  According  to  Laplace, 
the  material  of  our  solar  system  was  once  a  nebulous  mass 
of  extreme  tenuity,  and  the  sun,  moon,  and  planets  were 
formed  by  its  gradual  condensation.  Let  us  suppose  such 
a  nebulous  mass  slowly  rotating,  and  gradually  cooling  by 


CONSERVATION    OF    ENERGY.  295 

radiation  into  space.  As  it  cools,  it  must  begin  to  con- 
tract ;  and  as  it  contracts,  its  rotation  must  be  quickened, 
since  the  matter  at  the  surface  must  be  moving  faster  than 
nearer  the  centre.  It  thus  goes  on  contracting  and  rotat- 
ing faster  and  faster,  until  the  centrifugal  tendency  becomes 
so  great  that  cohesion  and  gravity  can  no  longer  hold  it 
together.  A  ring  is  then  detached  from  the  circumfer- 
ence, which  continues  to  rotate  by  itself.  The  central 
mass  goes  on  contracting  and  rotating  with  ever-increasing 
velocity,  until  a  second  ring  is  thrown  off.  In  this  way, 
ring  after  ring  is  detached,  and  all  these  rings  continue  to 
rotate  round  the  central  mass  in  the  same  direction.  But 
the  rings  themselves  would  go  on  condensing,  and  at  last 
they  would  be  likely  to  break  up,  each  forming  one  or  sev- 
eral globular  masses.  These  would,  of  course,  all  revolve 
about  the  central  mass  in  the  same  direction,  and  their 
condensation  would  cause  them  to  rotate  on  their  axes  ; 
and  it  has  been  proved  that,  with  the  exception  of  one  or 
two  of  the  outer  ones,  they  must  all  rotate  on  their  axes  in 
the  same  direction  in  which  they  revolve  in  their  orbits. 

But  as  these  masses  condensed,  their  rotation  would  be 
accelerated,  and  they  would  be  very  likely  to  throw  off 
rings,  which  would  either  remain  as  rings,  or  be  condensed 
into  secondary  masses  revolving  about  their  primaries. 

The  central  mass,  of  course,  forms  the  sun ;  the  rings 
which  it  throws  off,  the  planets ;  and  the  rings  thrown  off 
by  the  planets,  the  moons.  In  the  case  of  Saturn,  a  part 
of  the  rings  still  remain  uncondensed,  while  a  part  appear 
as  moons. 

The  rings  thrown  off  by  the  central  mass  usually  con- 
densed into  one  body,  but,  in  the  case  of  th:.  minor  plan- 
ets and  the  meteoric  rings,  into  many. 

234.  Helmholttfs  Theory  of  Solar  Heat.  —  The  nebular 
hypothesis  not  only  accounts  for  the  motion  of  the  planets, 
but  it  explains  the  internal  heat  of  the  earth  and  the  solar 


296  CONSERVATION    OF    ENERGY. 

heat ;  for,  as  the  molecules  of  the  nebulous  mass  'were 
drawn  nearer  and  nearer  together,  their  potential  energy 
must  have  been  converted  into  heat.*  Helmholtz  has 
made  this  the  basis  of  his  theory  of  solar  heat,  an  account 
of  which  is  given  by  Tyndall  as  follows  :  — 

"  He  starts  from  the  nebular  hypothesis  of  Laplace,  and, 
assuming  the  nebulous  matter  in  the  first  instance  to  have 
been  of  extreme  tenuity,  he  determines  the  amount  of  heat 
generated  by  its  condensation  to  the  present  solar  system. 
Supposing  the  -specific  heat  of  the  condensing  mass  to  be 
the  same  as  that  of  water,  then  the  heat  of  condensation 
would  be  sufficient  to  raise  their  temperature  28,000,000° 
Centigrade.  By  far  the  greater  part  of  this  heat  was 
wasted  ages  ago  in  space.  The  most  intense  terrestrial 
combustion  that  we  can  command  is  that  of  oxygen  and 
hydrogen,  and  the  temperature  of  the  pure  oxyhydrogen 
flame  is  8,06 1°  C.  The  temperature  of  a  hydrogen  flame, 
burning  in  air,  is  3,259°  C. ;  while  that  of  the  lime-light, 
which  shines  with  such  sunlike  brilliancy,  is  estimated  at 
2,000°  C.  What  conception,  then,  can  we  form  of  a  tem- 
perature more  than  thirteen  thousand  times  that  of  the 
Drummond  light  ?  If  our  system  were  composed  of  pure 
coal  and  burnt  up,  the  heat  produced  by  its  combustion 
would  only  amount  to  -^  of  that  generated  by  the*  con- 
densation of  the  nebulous  matter  to  form  our  solar  system. 
Helmholtz  supposes  this  condensation  to  continue  ;  that  a 
virtual  falling  down  of  the  superficial  portions  of  the  sun 
towards  the  centre  still  takes  place,  a  continual  develop- 
ment of  heat  being  the  result.  However  this  may  be,  he 
shows  by  calculation  that  the  shrinking  of  the  sun's  di- 
ameter by  -—  of  its  present  length  would  generate  an 

*  It  would  seem  at  first  that  this  heat  would  prevent  further  con- 
densation, but  it  is  gradually  radiated  off  into  space,  and  as  the  mole- 
cules come  nearer  together  the  force  of  gravity  increases  more  rapidly 
than  the  repulsive  force  of  the  remaining  heat. 


CONSERVATION    OF    ENERGY.  297 

amotint  of  heat  competent  to  cover  the  solar  emission  for 
2,000  years  ;  while  the*  shrinking  of  the  sun  from  its  pres- 
ent mean  density  to  that  of  the  earth  would  have  its  equiv- 
alent in  an  amount  of  heat  competent  to  cover  the  present 
solar  emission  for  17,000,000  of  years. 

"  <  But,'  continues  Helmholtz,  '  though  the  store  of  our 
planetary  system  is  so  immense  that  it  has  not  been  sensi- 
bly diminished  by  the  incessant  emission  which  has  gone 
on  during  the  period  of  man's  history,  and  though  the  time 
which  must  elapse  before  a  sensible  change  in  the  condi- 
tion of  our  planetary  system  can  occur  is  totally  beyond 
our  comprehension,  the  inexorable  laws  of  mechanics  show 
that  this  store,  which  can  only  suffer  loss  and  not  gain, 
must  finally  be  exhausted.  Shall  we  terrify  ourselves  by 
this  thought  ?  We  are  in  the  habit  of  measuring  the 
greatness  of  the  universe,  and  the  wisdom  displayed'in  it, 
by  the  duration  and  the  profit  which  it  promises  to  our 
own  race  ;  but  the  past  history  of  the  earth  shows  the  in- 
significance of  the  interval  during  which  man  has  had  his 
dwelling  here.  What  the  museums  of  Europe  show  us  of 
the  remains  of  Egypt  and  Assyria  we  gaze  upon  with  silent 
wonder,  in  despair  of  being  able  to  carry  back  our  thoughts 
to  a  period  so  remote.  Still,  the  human  race  must  have 
existed  and  multiplied  for  ages  before  the  Pyramids  could 
have  been  erected.  We  estimate  the  duration  of  human 
history  at  6,000  years ;  but,  vast  as  this  time  may  appear 
to  us,  what  is  it  in  comparison  with  the  period  during 
which  the  earth  bore  successive  series  of  rank  plants  and 
mighty  animals,  but  no  men  ?  —  periods  during  which,  in 
"nir  own  neighborhood  (Konigsberg),  the  amber -tree 
bloomed,  and  dropped  its  costly  gum  on  the  earth  and 
in  the  sea ;  when  in  Europe  and  North  America  groves 
of  tropical  palms  flourished,  in  which  gigantic  lizards,  and, 
after  them,  elephants,  whose  mighty  remains  are  still  buried 
in  the  earth,  found  a  home.  Different  geologists,  proceed- 
13* 


298  CONSERVATION    OF    ENERGY. 

ing  from  different  premises,  have  sought  to  estimate  the 
length  of  the  above  period,  and  they  set  it  down  from  one 
to  nine  millions  of  years.  The  time  during  which  the 
earth  has  generated  organic  beings  is  again  small  com- 
pared with  the  ages  during  which  the  world  was  a  mass  of 
molten  rocks.  The  experiments  of  Bischof  upon  basalt 
show  that  our  globe  would  require  350  millions  of  years  to 
cool  down  from  2,000°  to  200°  Centigrade.  And  with 
regard  to  the  period  during  which  the  first  nebulous 
masses  condensed,  to  form  our  planetary  system,  conjec- 
ture must  entirely  cease.  The  history  of  man,  therefore, 
is  but  a  minute  ripple  in  the  infinite  ocean  of  time.  For 
a  much  longer  period  than  that  during  which  he  has  al- 
ready occupied  this  world,  the  existence  of  a  state  of  inor- 
ganic nature,  favorable  to  man's  continuance  here,  seems 
to  be  secured  ;  so  that  for  ourselves,  and  for  long  genera- 
tions after  us,  we  have  nothing  to  fear.  But  the  same 
forces  of  air  and  water,  and  of  the  volcanic  interior,  which 
produced  former  geologic  revolutions,  burying  one  series 
of  living  forms  after  another,  still  act  upon  the  earth's 
crust.  They,  rather  than  those  distant  cosmical  changes 
of  which  we  have  spoken,  will  put  an  end  to  the  human 
race,  and  perhaps  compel  us  to  make  way  for  new  and 
more  complete  forms  of  life,  as  the  lizard  and  the  mam- 
moth have  given  way  to  us  and  our  contemporaries/  " 

It  will  be  noticed  that  Mayer's  theory  is  not  inconsistent 
with  that  of  Helmholtz,  but  supplementary  to  it.  The 
former  merely  assumes  that  the  meteors  and  planets,  which 
were  thrown  off  from  the  nebulous  mass  as  it  condensed, 
are  slowly  falling  into  it  again.  When  these  shall  all  have 
fallen  into  it  and  the  condensation  shall  have  ceased,  our 
sun  will  cease  to  shine,  like  many  other  stars  which  have 
disappeared  from  the  heavens. 


ASTRONOMY.  299 


SUMMARY. 

When  bodies  or  their  molecules  are  in  motion,  they  are 
said  to  have  an  actual  energy  •  and  when  they  are  so  situ- 
ated that  they  can  be  moved  by  gravity  or  by  the  molecu- 
lar forces,  they  are  said  to  have  a  potential  energy.  (215.) 

Energy  may  be  mechanical,  molecular,  or  muscular. 
(216.) 

Affinity,  cohesion,  and  gravity  are  the  forces  which  are 
constantly  tending  to  convert  potential  into  actual  energy. 

(217.) 

Heat  is  not  a  substance,  but  only  a  mode  of  motion,  as 
was  shown  by  Count  Rumford  and  by  Sir  Humphrey 
Davy.  (219,  220.) 

Mechanical  energy  may  be  converted  into  heat,  into 
which,  .in  fact,  all  mechanical  energy  is  ultimately  con- 
verted. (218,  221.) 

The  same  amount  of  mechanical  energy,  on  conversion 
into  heat,  always  gives  rise  to  the  same  amount  of  heat. 

(222.) 

Heat  may  be  again  converted  into  mechanical  energy  ; 
and  the  same  amount  of  heat  always  gives  rise  to  the  same 
amount  of  mechanical  energy.  (223,  224.) 

The  energy  of  affinity  is  converted  partially  into  elec- 
tricity, partially  into  heat,  and  partially  into  muscular  en- 
ergy. (225-228.) 

The  strength  of  affinity  is  shown  by  tlie  great  amount  of 
heat  generated  in  the  burning  of  hydrogen  and  carbon. 


However  energy  may  be  transmuted,  it  can  never  be 
destroyed.  (229.) 

All  the  energy  manifested  at  the  surface  of  the  earth, 
except  that  of  the  tides,  is  drawn  from  the  sunbeams. 


300  ASTRONOMY. 

The  sun  radiates  sufficient  heat  to  melt  a  cylinder  of  ice 
45  miles  thick,  at  the  rate  of  190,000  miles  a  second. 


According  to  Mayer,  the  solar  heat  is  developed  by 
meteoric  showers  ;  according  to  Helmholtz,  by  the  grad- 
ual condensation  of  the  sun.  (232  -  234.) 


APPENDIX. 


APPENDIX 


Fig.  i. 


I. 


1.  A  right  triangle  is  one  which  contains  a  right  angle. 
Thus  A  C  J3,  Figure  I,  is  a  right 

triangle. 

2.  An  oblique  triangle  is  one  which 
does  not  contain  a  right  angle. 

Every  oblique  triangle  can  be  re- 
solved into  two  right  triangles  by 
dropping  a  perpendicular  from  one 
of  the  angles  upon  the  opposite  side. 

Thus  in  Figure  2,  by  dropping  the 
perpendicular  C  P,  two  right  trian- 
gles, A  P  C  and  B  P  C,  are  formed. 

In  Figure  3,  by  dropping  the  per- 
pendicular B  P  upon  A  C  produced,      i 
we  get  two  right  triangles,  A  P  B 
and  C  P  B. 

2.  The  sine  of  an  angle  is  the  quo- 
tient of  the  opposite  side  divided  by 
the  hypothenuse.  —  Thus,  by  desig- 
nating the  angles  by  the  large  let- 
ters and  the  sides  opposite  them 
by  the  corresponding  small  ones,  we  /- 
have  in  Figure  i, 


Fig.  2. 


Fig.  3- 


sin  A  =  -,    sin  B 


and  sin  C 


The  sine  of  a  right  angle  equals  unity. 


3°4 


APPENDIX. 


In  Figures  2  and  3,  we  have 

s~*  T)  s*  r>  T?  zy 

sin  A  =  -.-•-.  sin  B  =  —  ,  and  sin  C  =  —  . 
t>  a  a 

BCA+BCP  =  180°. 

When  the  sum  of  two  angles  is  180°,  the  angles  are  said 
to  be  supplements  of  each  other. 

/?  7-* 

It  will  be  seen  that,  in  Figure  3,  -  -  is   the  sine   of  both 
B  C  A  and  B  C  P. 

An  angle  and  its  supplement  have  the  same  sine. 

3.  The  sides  of  a  plane  triangle  are  proportional  to  the  sines 
of  their  opposite  angles. 

In  Figure  i,  we  have 

c  sin  A.  c 


B      .      A        a 
sm  A  =  -,  a 


c  sin 


c  sin  C.  c 


sin  A 
b 

c 
sin  C 


whence 


sin  A 

a 
sin  A 

b 
sin  B 


b 
sin  B 

c 
sin  C 

c 


sin  C 
which,  converted  into  proportions,  give 


a 

sin  A  =  b 

sin  B 

a 

sin  A  =  c 

sin  C 

b 

sin  B  =  c 

sin  C 

and  these,  by 

transposi 

ng  the  mean 

s,  give 

a 

b  =  sin  A 

sin  B 

a 

c  =  sin  A 

sin  C 

b 

c  =  sin  B 

sin  C 

In  Figure  2,  we  have 

.*f.cr. 

-CP<  CP  = 


b  sin  A 


whence 


b  sin  ^4  =  a  sin 


APPENDIX.  305 

which,  converted  into  a  proportion,  gives 

a  :  b  =  sin  A  :  sin  B. 
In  Figure  3,  we  have 
sin  A  =  ~,  B  P  =  c  sin  A 

sin  C  =  —,  B  P  =  a  sin  C 

a 

whence  a  sin  C  =  c  sin  A 

which,  converted  into  a  proportion,  gives 

a  :  c  =  sin  A  :  sin  C. 

By  dropping  a  perpendicular  from  A  upon  Z?  C  produced, 
it  can  be  found  in  the  same  way  that 

b  :  c  =  sin  B  :  sin  C 

In  both  right  and  oblique  triangles,  then,  the  sides  are  pro- 
portional to  the  sines  of  their  opposite  angles, 

4.  It  is  shown  in  Geometry  that  two  right  triangles  which 
have   an  acute  angle  of  one  equal  to  an  acute  angle  of  the 
other,   have  their   corresponding  sides  proportional.      Hence 
whatever  the  length  of  the  sides  b  and  c  in  the  right  triangle, 

Figure  i,  -  and  -  will  have  the  same  values  as  long  as  the  an- 
gles A  and  B  remain  the  same.  The  value  of  the  sine,  then, 
depends  wholly  on  the  size  of  the  angle. 

The  value  of  the  sines  have  been  computed  for  every  an- 
gle between  o°  and  90°,  and  these  values  have  been  arranged 
in  tables  called  "  Tables  of  Natural  Sines." 

5.  By  means  of  (3),  the  other  parts  of  a  plane  triangle  can 
be  found  when  one  side  and  two  angles  are  given. 

To  find  the  third  angle,  subtract  the  sum  of  the  given  an- 
gles from  1 80°. 

To  find  ,the  other  sides,  form  a  proportion  as  follows  :  As 
the  sine  of  the  angle  opposite  the  given  side  is  to  the  sine  of 
the  angle  opposite  the  required  side,  so  is  the  given  side  to 
the  required  side. 

Thus  in  the  triangle  ABC,  Figure  2,  given  the  side  a,  and 
the  angles  B  and  C. 

To  find  the  angle  A. 

180°  —  (B  -4-  Q  =  A. 

T 


306  APPENDIX. 

To  find  the  side  b. 

sin  A  :  sin  B  =  a  :  b. 

Find  the  side  c. 

Since  one  of  the  angles  of  a  right  triangle  is  always  a  right 
angle,  the  parts  of  such  a  triangle  can  be  computed  when  one 
side  and  one  acute  angle  are  given. 

In  the  right  triangle  ABC,  Figure  I,  given  the  side  c  and 
fthe  angle  A.  Find  the  other  parts. 

6.  By  means  of  (3),  the  other  parts  of  a  plane  triangle  can 
!be  computed  when  two  sides  and  an  angle  opposite  one  of  them 
are  given. 

To  find  a  second  angle,  form  the  following  proportion :  As 
the  side  opposite  the  given  angle  is  to  the  side  opposite  the 
required  angle,  so  is  the  sine  of  the  given  angle  to  the  sine 
of  the  required  angle. 

After  the  second  angle  is  found  the  case  becomes  the  same 
as  (5). 

In  the  triangle  A  B  C,  Figure  2,  given  a  and  c  and  the  an- 
gle A.  Find  B,  C,  and  b. 

II. 

The  horizon  is  the  plane  which  at  any  point  on  the  earth 
would  separate  the  visible  from  the  invisible  part  of  the  heav- 
ens, if  the  earth  were  everywhere  level  like  the  surface  of  the 
sea.  It  divides  the  celestial  sphere  into  two  equal  parts,  and 
its  intersection  with  it  forms  the  circumference  of  a  great  circle. 
Every  part  of  this  circumference  is  90°  from  the  zenith. 

At  the  equator  the  celestial  poles  are  just  90°  from  the  ze- 
nith, hence  the  horizon  will  pass  through  these,  and  its  plane 
will  coincide  in  direction  with  the  earth's  axis.  As  we  go 
north  from  the  equator,  the  zenith  passes  northward,  and  the 
horizon  passes  below  the  north  pole  and  becomes  more  and 
more  inclined  to  the  earth's  axis  till  we  reach  the  pole,  when 
the  inclination  becomes  90°.  As  we  go  southward  from  the 
equator,  a  corresponding  change  takes  place. 


APPENDIX.  307 


III. 


THE    CALENDAR. 

OLD    AND    NEW    STYLE. 

THE  solar  year,  or  the  interval  between  two  successive  pas- 
sages of  the  same  equinox  by  the  sun,  is  365  days,  5  hours, 
48  minutes,  48  seconds.  If  then  we  reckon  only  365  days  to  a 
common  or  civil  year,  the  sun  will  come  to  the  equinox  5  hours, 
48  minutes,  48  seconds,  or  nearly  a  quarter  of  a  day,  later  each 
year ;  so  that,  if  the  sun  entered  Aries  on  the  2oth  of  March 
one  year,  he  would  enter  it  on  the  2ist  four  years  after,  on  the 
22d  eight  years  after,  and  so  on.  Thus  in  a  comparatively 
short  time  the  spring  months  would  come  in  the  winter,  and 
the  summer  months  in  the  spring. 

Among  different  ancient  nations  different  methods  of  com- 
puting the  year  were  in  use.  Some  reckoned  it  by  the  revo- 
lutions of  the  moon  ;  some  by  that  of  the  sun :  but  none,  so 
far  as  we  know,  made  proper  allowances  for  deficiencies  and 
excesses.  Twelve  moons  fell  short  of  the  true  year ;  thirteen 
exceeded  it :  365  days  were  not  enough ;  366  were  too  many. 
To  prevent  the  confusion  resulting  from  these  errors,  Julius 
Caesar  reformed  the  calendar  by  making  the  year  consist  of 
365  days,  6  hours  (which  is  hence  called  a  Julian  year),  and 
made  every  fourth  year  consist  of  366  days.  This  method  of 
reckoning  is  called  Old  Style. 

But  as  this  made  the  year  somewhat  too  long,  and  the  error 
in  1582  amounted  to  ten  days,  Pope  Gregory  XIII.,  in  order  to 
bring  the  vernal  equinox  back  to  the  2ist  of  March  again,  or- 
dered ten  days  to  be  struck  out  of  that  year  ;  calling  the  next 
clay  after  the  4th  of  October  the  I5th.  And  to  prevent  similar 
confusion  in  the  future  he  decreed  that  three  leap-years  should 
be  omitted  in  the  course  of  every  400  years.  This  way  of 
reckoning  time  is  called  New  Style.  It  was  immediately 
adopted  by  most  of  the  European  nations,  but  was  not  accepted 


308  APPENDIX. 

by  the  English  until  the  year  1752.  The  error  then  amounted 
to  ii  days,  which  were  taken  from  the  month  of  September,  by 
calling  the  3d  of  that  month  the  Hth. 

According  to  the  Gregorian  calendar,  every  year  whose  num- 
ber is  divisible  by  4  is  a  leap-year;  except  that  in  the  case  of  the 
years  whose  numbers  are  exact  hundreds,  those  only  are  leap- 
years  which  are  divisible  by  4  after  cutting  off  the  last  two 
figures.  Thus,  the  years  1600,  2000,  2400,  etc.,  are  leap-years  ; 
1700,  1800,  1900,  2100,  2200,  etc.,  are  not.  Under  this  mode  of 
reckoning,  the  error  will  not  amount  to  a  day  in  5,000  years. 

THE  DOMINICAL  LETTER. 

The  Dominical  Letter  for  any  year  is  that  which  we  often  see 
placed  against  Sunday  in  the  almanacs,  and  is  always  one  of 
the  first  seven  in  the  alphabet.  Since  a  common  year  consists 
of  365  days,  if  this  number  be  divided  by  7,  the  number  of  days 
in  a  week,  there  will  be  a  remainder  of  one.  Hence  a  year 
commonly  begins  one  day  later  in  the  week  than  the  preced- 
ing one  did.  If  a  year  of  365  days  begins  on  Sunday,  the  next 
will  begin  on  Monday ;  if  it  begins  on  Thursday,  the  next  will 
begin  on  Friday;  and  so  on.  If  Sunday  falls  on  the  ist  of 
January,  the  first  letter  of  the  alphabet,  or  A,  is  the  Dominical 
Letter.  If  Sunday  falls  on  the  7th  of  January  (as  it  will  the 
next  year,  unless  the  first  be  leap-year)  the  seventh  letter,  G,  is 
the  Dominical  Letter.  If  Sunday  falls  on  the  6th  of  January 
(as  it  will  the  third  year,  unless  the  first  or  second  be  leap-year) 
the  sixth  letter,  F,  will  be  the  Dominical  Letter.  Thus,  if  there 
were  no  leap-years,  the  Dominical  Letters  would  regularly  fol- 
low a  retrograde  order,  G,  F,  E,  D,  C,  B,  A. 

But  leap  years  have  366  days  ;  which,  divided  by  7,  leaves  2 
remainder.  Hence  the  years  following  leap-years  will  begin 
two  days  later  in  the  week  than  the  leap-years  did.  To  prevent 
the  interruption  which  would  hence  occur  in  the  order  of  the 
Dominical  Letters,  leap-years  have  two  Dominical  Letters ; 
one  indicating  Sunday  till  the  29th  of  February,  and  the  other 
for  the  rest  of  the  year. 

By  Table  I.  below,  the  Dominical  Letter  for  any  year  (New 
Style)  for  4,000  years  from  the  beginning  of  the  Christian 


APPENDIX. 


309 


Era  may  be  found ;  and  it  will  be  readily  seen  how  the  Table 
could  be  extended  indefinitely. 

To  find  the  Dominical  Letter  by  this  Table,  look  for  the  hun- 
dreds of  years  at  the  top,  and  for  the  years  below  a  hundred  at 
the  left  hand. 


TABLE  I. 

TABLE  II. 

Centuries. 

A    B 

C 

D 

E 

F 

G 

100     200 

500   600 

300  400 

700  800 

I       2 

3 

4 

5 

6 

7 

900  1000 

IIOO'l2OO 

Jan.  31. 

8     9 

IO 

ii 

12 

13 

H 

Years  less  than 
One  Hundred. 

1300  1400 
1700'  1800 

2100  2200 
2500  26OO 

I500 

1900 
2300 
2700 

1600 

2OOO 
2400 
2800 

Oct.  31. 

15    16 

22    23 
29    30 

17 

24 

18 

25 

19 
26 

20 
27 

21 

28 

29003000 

3IOO 

3200 

T 

2 

« 

A 

33003400 
3700  3800 

3500 
3000 

3boo 

4000 

Feb.  28-29. 

5 

6 

7 

8 

9 

10 

ii 

C 

E 

G 

BA 

March  31. 

12 

H 

ib 

17 

18 

I 

29 

57 

85 
86 

B 

D 

r' 

F 

G 

Nov.  30. 

26 

27 

28 

29 

30 

-4 

3* 

.. 

3 

31 

5Q 

87 

G 

B 

D 

E 

i 

4 

I 

7 

1^ 

33 
34 
35 

61 
62 
63 

88 

89 
90 
91 

FE 
D 
C 
B 

AG 

F 
E 
D 

CB 
A 
G 
F 

DC 
B 
A 
G 

April  30. 

July  31 

2 

9 
16 

23 

3 

IO 

24 

4 
ii 

18 

5 

12 
19 
26 

6 

*3 
20 

27 

7 

H 

21 

28 

8 
15 

22 
29 

\C, 

C  P, 

ED 

FE 

6^ 

<J 

*     * 

"  • 

*     ' 

9 

° 

37 

65 

92 
93 

F 

"AT 

TT 

•j. 

7 

.1 

8 

2 

9 

•J 

IO 

4 

IT 

5 

T2 

10 

ii 

12 

39 
40 

66 
67 
68 

94 
95 
96 

D 
CB 

G 
F 
ED 

B 
A 
GF 

C 
B 
AG 

Aug.  31. 

20 

?7 

H 

21 

28 

15 
22 

29 

16 

23 
30 

17 

24 

31 

18 
25 

26 

n 

41 

69 

97 

A 

C 

E 

I 

I 

2 

H 

n 

42 
43 
44 

70 

71 
72 

98 
99 

G 
F 
ED 

B 
A 

GF 

D 

C 

BA 

E 
D 
CB 

Sept.  30. 

•3 

10 

4 
ii 
18 

•  5 

12 
IQ 

6 
13 

20 

7 
H 

21 

8 

22 

,1 

23 

17 

45 

73 

C 

E 

c; 

A 

Dec.  31. 

24 

2S 

26 

27 

28 

2$ 

30 

18 

46 

74 

B 

D 

F 

G 

19 

47 

75 

A 

C 

E 

F 

j 

2       3 

6 

20 

48 

76 

GF 

BA 

DC 

ED 

7 

8 

9  10 

II 

12 

13 

21 

4') 

77 

.  . 

E 

G 

B 

C 

May  31. 

H 

15.16!  17 

18  19 

20 

22 

50 

78 

D 

F 

A 

B 

21 

22  '  23  I  24 

25  26 

27 

27 

c  i 

7Q 

C 

|V 

/~V 

A 

"S 

2O    IO  i  31 

24 

52 

80 

BA 

DC 

FE 

GF 

I       2 

T. 

25 

53 

IT 

T7 

G 

IT 

~D~~E~ 

4 

5 

6 

7 

8     9 

IO 

26 

54 

82 

F 

A 

C     D 

June  30. 

ii 

12  '13 

14 

IS 

16 

17 

27 

55 

8s 

E 

G 

B    C 

18 

19    2O 

21 

22 

23 

24 

28 

56 

84 

..  'DCFE 

AGBA 

25 

26    27 

28 

29 

3° 

310  APPENDIX. 

Thus,  the  letter  for  1867  will  be  opposite  the  number  67,  and 
in  the  column  having  1800  at  the  top  ;  that  is,  it  will  be  F.  In 
the  same  way,  the  letters  for  1868,  which  is  a  leap-year,  will 
be  found  to  be  ED. 

Having  the  Dominical  Letter  of  any  year,  Table  II.  shows 
what  days  of  every  month  of  the  year  will  be  Sundays. 

To  find  the  Sundays  of  any  month  in  the  year  by  this  Table, 
look  in  the  column  under  the  Dominical  Letter,  opposite  the 
name  of  the  month  given  at  the  left. 

From  the  Sundays  the  date  of  any  other  day  of  the  week  can 
be  readily  found. 

Thus  if  we  wish  to  know  on  what  day  of  the  week  Christmas 
will  fall  in  1867,  we  look  opposite  December  under  the  letter  F, 
(which  we  have  found  to  be  the  Dominical  Letter  for  the  year,) 
and  find  that  the  22d  of  the  month  is  a  Sunday.  The  25th,  or 
Christmas,  will  then  be  Wednesday. 

In  the  same  way  we  may  find  the  day  Of  the  week  corre- 
sponding to  any  date  (New  Style)  in  history.  For  instance,  the 
I7th  of  June,  1775,  the  day  of  the  fight  at  Bunker  Hill,  is  found 
to  have  been  a  Saturday. 

These  two  Tables  then  serve  as  a  perpetual  almanac. 

THE  GOLDEN  NUMBER. 

It  has  been  found  that  after  a  period  of  19  years  the  sun, 
earth,  and  moon  occupy  nearly  the  same  relative  positions. 
Starting  then  with  new  moon  or  full  moon,  it  is  evident  that 
after  the  expiration  of  this  period  it  will  be  new  moon  or  full 
moon  again.  Hence  the  phases  of  the  moon  which  succeed- 
ed one  another  in  the  first  period  will  repeat  themselves  in 
the  same  order  in  the  second. 

This  period  is  called  the  Cycle  of  the  Moon,  and  the  number 
19  is  known  as  the  Golden  Number. 

To  find  the  Golden  Number  for  any  year,  add  I  to  the  num- 
ber of  that  year,  divide  by  19,  and  the  remainder  is  the  Golden 
Number.  If  nothing  remains,  the  Golden  Number  is  19. 

In  Table  III.  the  Golden  Numbers  under  the  months  stand 
against  the  days  of  new  moon  in  the  left  hand  column.  It  is 
adapted  chiefly  to  the  second  year  after  leap  year,  and  will  in- 


APPENDIX.  311 

dicate  the  time  of  new  moon  (within  one  day)  till  the  year  1900. 
A  perfectly  correct  table  of  this  kind  cannot  be  easily  made. 

To  show  the  use  of  the  Table,  suppose  we  wish  to  know 
nearly  the  time  of  new  moon  in  September,  1867.  By  the  rule 
given  above,  we  find  the  Golden  Number  for  the  year  to  be  6. 
Looking  in  the  Table  under  September,  we  find  the  number  6 
opposite  the  27th  day  of  the  month. 

The  error  can  in  no  case  exceed  one  day. 


TABLE  III. 


I 

>» 

1 

>—  » 

February. 

j~ 
£ 

PS 

I 

|h 

rt 

§ 
•—  » 

>, 

's 
>—  > 

ti 

1 

< 

September. 

October. 

1 
£ 

December. 

I 

~9~ 

9 

17 

17 

II 

19 

2 

17 

-  .  . 

6 

H 

H 

3 

II 

19 

3 

17 

6 

17 

'.6 

3 

ii 

19 

8 

*8 

4 

6 

6 

H 

H 

3 

.  . 

ig 

8 

.  . 

16 

H 

3 

ii 

n 

19 

8 

16 

6 

H 

3 

14 

3 

19 

16 

5 

5 

7 

3 

3 

ii 

ii 

19 

'i 

16 

13 

8 

ii 

19 

8 

8 

16 

5 

5 

13 

9 

ii 

19 

ii 

19 

'3 

2 

10 

19 

8 

| 

16 

1  6 

5 

13 

2 

IO 

ii 

19 

8 

5 

J3 

2 

2 

IO 

12 

8 

16 

's 

16 

16 

5 

10 

18 

13 

.  . 

5 

13 

13 

2 

10 

18 

7 

H 

16 

5 

16 

5 

2 

IO 

18 

is 

7 

15 

5 

5 

13 

13 

2 

7 

15 

16 

!3 

2 

10 

10 

18 

7 

15 

17 

13 

2 

13 

2 

18 

7 

15 

4 

4 

18 

2 

2 

IO 

10 

18 

15 

12 

19 

IO 

.  . 

18 

7 

7 

15 

4 

4 

12 

20 

IO 

18 

IO 

18 

15 

12 

I 

I 

21 

18 

18 

7 

7 

15 

4 

12 

9 

22 

7 

15 

4 

4 

12 

I 

I 

9 

23 

7 

15 

7 

15 

12 

9 

17 

17 

24 

15 

4 

4 

12 

I 

9 

6 

25 

15 

4 

12 

I 

9 

i? 

17 

*6 

26 

4 

4 

12 

I 

6 

.  . 

H 

27 

12 

I 

I 

9 

9 

17 

'6 

.  . 

H 

28 

12 

I 

12 

9 

17 

6 

H 

H 

3 

3 

29 

I 

I 

9 

17 

3 

ii 

30 

17 

6 

'e 

14 

3 

ii 

31 

9 

•• 

9 

•• 

•• 

H 

3 

•  • 

ii 

19 

312 


APPENDIX. 


EPACT. 

A  solar  year,  as  we  have  seen,  is  about  365  days,  6  hours  ;  a 
lunar  year,  of  12  lunar  months,  is  about  354  days,  9  hours. 
The  difference  of  nearly  u  days  between  the  two  is  the  An- 
nual Epact.  Since  the  epact  of  one  year  is  n  days,  that  of  2 
years  will  be  22  days  ;  of  3  years  33  days,  or  rather  3  days,  be- 
ing 3  days  over  a  lunar  month.  Thus,  by  yearly  adding  n, 
and  casting  out  the  3o's,  it  will  be  found  that  on  every  igth 
year  29  remains  ;  which  is  reckoned  a  complete  lunar  month, 
and  the  epact  is  o.  Thus  the  cycle  of  epacts  expires  with  the 
lunar  cycle,  or  that  of  the  Golden  Numbers  ;  and  on  every  igth 
year  the  solar  and  lunar  years  begin  together. 

By  the  epact  of  any  year  the  moon's  age  (115)  for  the  \st 
of  January  is  shown. 

Table  IV.  gives  the  Golden  Numbers  with  the  corresponding 
Epacts  till  the  year  1900. 

TABLE  IV. 


Golden 
No. 

Epact. 

Golden 
No. 

Epact. 

Golden 
No. 

Epact. 

Golden 
No. 

Epact. 

Golden 
No. 

Epact. 

, 

O 

5 

H 

9 

28 

13 

12 

17 

26 

2 

II 

6 

25 

IO 

9 

14 

23 

18 

7 

3 

22 

7 

6 

II 

20 

15 

4 

19 

18 

4 

3 

8 

17 

12 

1 

16 

15 

IV. 


THE   METRIC    SYSTEM. 

SINCE  the  measurement  of  length  is  required  for  almost 
every  purpose  of  construction,  as  well  as  for  every  intelligible 
statement  of  the  size  of  material  objects  and  their  distance  from 
one  another,  it  is  indispensable  that  every  community  should 
fix  upon  some  common  standard,  some  well  known  unit,  by 
whose  repetition  and  subdivision  length,  distance,  and  size, 
whether  great  or  small,  can  be  expressed  in  words  and 
numbers. 


APPENDIX.  3 13 

The  standards  which  almost  all  communities  have  taken 
for  their  unit  of  length,  have  been  either  some  portion  of 
the  human  body,  such  as  the  length  of  the  arm,  of  the  fore- 
arm (the  ell  or  cubit),  of  the  foot,  of  the  breadth  of  the  hand 
(span  or  palm),  or  the  length  of  the  ordinary  step  (pace) ; 
and  for  measuring  smaller  lengths,  the  length  of  certain 
cereal  grains,  such  as  those  of  rice  or  barley  (the  barley- 
corn}. 

Thus  an  old  English  statute  defined  an  inch  as  the  length 
of  three  barleycorns. 

But  no  part  of  the  body  of  a  full  grown  man  has  invariably 
the  same  length  ;  hence  it  became  necessary  for  each  com- 
munity to  take  the  length  of  a  particular  fore-arm  or  foot  for 
their  unit.  In  this  way  the  units  fixed  upon  by  different  com- 
munities did  not  agree  with  one  another.  Thus  we  find  the 
length  of  the  Roman  foot  equivalent  to  1 1.6  of  our  inches  ;  the 
English  to  12  ;  the  Grecian  to  12.1  ;  the  French  to  12.8  ;  and 
the  Egyptian  to  13.1. 

The  English  unit  is  the  yard,  which  is  said  to  have  been  in- 
troduced by  King  Henry  the  First,  who  ordered  that  the  ulna, 
or  ancient  ell,  which  corresponds  to  the  modern  yard,  should 
be  made  the  exact  length  of  his  own  arm,  and  that  the  other 
measures  of  length  should  be  based  upon  it. 

In  1790,  at  the  time  of  the  French  Revolution,  that  people 
undertook  to  establish  a  new  metrical  system,  and  sought  for 
some  natural  object  of  invariable  length  upon  which  to  base 
their  unit  of  length.  They  chose  the  length  of  a  meridian  of 
the  globe,  and  they  called  the  ten- millionth  part  of  a  quadrant 
of  the  meridian  a  metre.  They  then  set  about  measuring  an 
arc  of  a  meridian  so  as  to  compute  exactly  the  length  of  its 
quadrant.  A  mistake  was  made  in  this  computation,  so  that 
the  French  metre  does  not  correctly  represent  the  ten-millionth 
part  of  the  quadrant  of  a  meridian. 

As  nations  come  into  closer  relations  with  one  another,  it 
becomes  more  and  more  desirable  that  they  should  have  a 
common  metrical  system. 

Accordingly  many  governments,  and  among  them  our  own, 
have  enacted  that  the  French  metre  shall  be  regarded  as  a 
legal  unit  of  measure. 
14 


314  APPENDIX. 

There  are,  however,  objections  to  this  unit.  It  is  true  it  is 
based  upon  the  quadrant  of  a  meridian,  which  is  of  invariable 
length,  but  it  does  not  represent  a  ten-millionth  of  that  quad- 
rant accurately. 

We  have  already  seen  that  the  radius  or  diameter  of  the 
earth  is  the  natural  unit  with  which  we  begin  the  measurement 
of  the  distance  of  the  heavenly  bodies.  Hence  it  would  be 
much  more  convenient  that  the  unit  of  linear  measurement 
should  be  based  upon  the  diameter  of  the  earth  than  upon  the 
length  of  a  meridian,  and  it  would  be  a  great  objection  to  the 
French  metre  that  it  is  not  based  upon  the  length  of  the 
earth's  diameter,  even  if  it  represented  accurately  what  it  pro- 
fesses to  do. 

Now,  Sir  John  Herschel  has  called  attention  to  the  fact 
that  if  the  English  inch  were  made  .001  longer  than  it  now 
is,  then  50  such  inches  would  represent  almost  exactly  a  ten- 
millionth  part  of  the  polar  diameter  of  the  earth.  He  conse- 
quently proposes  50  such  inches  as  the  unit  of  measure,  and 
would  call  it  a  module.  This  seems  on  the  whole  the  most 
satisfactory  unit  that  has  been  proposed. 

It  has  been  proposed  that  the  length  of  a  pendulum  beating 
seconds  be  taken  as  the  unit  of  length.  This  unit  would  dif- 
fer but  little  from  the  metre. 

It  has  this  advantage  ;  that  it  is  much  easier  to  measure  the 
length  of  such  a  pendulum  accurately  than  to  measure  the  arc 
of  a  meridian.  But  the  length  of  the  pendulum  beating  sec- 
onds as  a  standard  of  length  has  the  same  disadvantage  that 
the  human  foot  has  for  the  same  purpose.  It  has  already  been 
seen  that  pendulums  which  beat  seconds  in  different  parts  of 
the  earth  are  not  all  of  the  same  length.  If  then  the  length  of 
a  seconds  pendulum  is  to  be  taken  as  a  standard,  it  must  be 
stated  at  what  particular  place  the  pendulum  is  to  beat  sec- 
onds. 

Having  decided  upon  a  unit  of  length  it  is  necessary  to 
decide  according  to  what  scale  this  unit  shall  be  multiplied 
or  divided.  The  French  have  multiplied  and  divided  their 
metre  on  the  decimal  scale,  as  the  following  table  shows. 


APPENDIX.  315 

TABLE  OF  LINEAR  MEASURE. 


10  millimetres 

=   I  centimetre 

10  centimetres* 

=  i  decimetre 

10  decimetres 

==   I  metre 

10  metres 

=  i  decametre 

10  decametres 

=  I  hectometre 

10  hectometres 

=   i  kilometre. 

The  names  of  the  higher  orders  of  units,  or  the  multiples  of 
the  metre,  are  formed  from  the  word  metre  by  means  of  pre- 
fixes taken  from  the  Greek  numerals  :  namely,  deca-(io),  hecto- 
(100),  £//<?-(  i, ooo). 

The  names  of  the  lower  orders  of  units,  or  the  subdivisions 
of  the  metre,  are  formed  in  a  similar  manner  by  means  of  pre- 
fixes taken  from  the  Latin  numerals:  namely,  deci-(iv\  centi- 
( i oo),  milli-(\  ,000). 

This  is  certainly  a  great  improvement  upon  our  clumsy  mul- 
tiplication and  subdivision  of  the  yard  and  foot. 

It  is  very  desirable  that  the  units  of  length,  of  capacity,  and 
of  weight,  should  be  connected  in  some  natural  manner.  This 
the  French  do  very  neatly.  The  cubic  decimetre  is  their  unit 
of  capacity,  and  is  called  a  litre.  This  litre  is  multiplied  and 
divided  decimally  in  the  same  way  as  the  metre,  as  is  seen  in 
the  following  table. 

TABLE  OF  MEASURES  OF  CAPACITY. 

10  millilitres  =  i  centilitre 

10  centilitres  =  decilitre 

10  decilitres  =  litre 

10  litres  =  decalitre 

10  decalitres  =  hectolitre 

10  hectolitres  =  kilolitre. 

The  names  of  the  higher  and  lower  orders  of  units  are  formed 
from  the  name  of  the  litre,  in  the  way  explained  under  the  pre- 
ceding table. 

They  have  taken  the  weight  of  a  cubic  centimetre  of  water, 

*  The  new  five-cent  piece  (1866)  is  2  centimetres  in  diameter,  and  weighs  5 
grammes. 


316  APPENDIX. 

at  a  temperature  of  4°  Centigrade  in  a  vacuum,  as  their  unit 
of  weight,  and  have  called  it  a  gramme.  This  also  they -mul- 
tiply and  divide  decimally,  according  to  the  following  table. 

TABLE  OF  WEIGHTS. 


10  milligrammes 
10  centigrammes 
10  decigrammes 
10  grammes 
10  decagrammes 
10  hectogrammes 


centigramme 

decigramme 

gramme 

decagramme 

hectogramme 

kilogramme. 


The  names  are  formed  from  the  word  gramme  by  means  of 
prefixes,  in  the  same  manner  as  those  in  the  other  tables. 

It  would  probably  be  impossible  to  improve  upon  the  method 
in  which  the  French  have  multiplied  and  subdivided  the  unit  of 
measure,  and  in  which  they  have  connected  the  units  of  length, 
capacity,  and  weight. 

Our  unit  of  weight  is  the  grain.  This  is  defined  as  the 
weight  of  such  an  amount  of  distilled  water  that,  at  a  tempera- 
ture of  62°  Fahrenheit,  252.46  such  grains  shall  fill  a  cubic 
inch.  A  pound  avoirdupois  contains  7,000  of  these  grains  ; 
and  an  imperial  gallon  of  distilled  water  at  a  temperature  of 
62°  F.  70,000  of  them.  This  gallon  is  our  unit  of  capacity. 
An  ounce  contains  437^  such  grains.  According  to  this  sys- 
tem a  cubic  foot  of  distilled  water  at  a  temperature  of  62° 
F.  contains  997.145  ounces,  falling  short  of  1,000  ounces  by 
nearly  three  ounces.  It  is  evident  that  nothing  could  be 
more  clumsy  than  the  way  in  which  we  connect  our  units  of 
weight,  of  capacity,  and  of  length. 

But,  Sir  John  Herschel  has  called  attention  to  the  fact  that 
if  our  inch,  and  consequently  our  foot,  were  increased  .001  in 
length,  then  a  cubic  foot  of  water  at  the  temperature  of  62°  F. 
would  contain  almost  exactly  1,000  ounces,  and  that  it  would 
require  only  the  slightest  change  in  the  value  of  the  ounce  to 
make  it  contain  exactly  1,000  ounces.  Thus  by  taking  the 
ounce  thus  slightly  modified  as  our  unit  of  weight,  it  would  be 
connected  decimally  with  our  unit  of  length.  Also  our  half- 
pint,  which  he  proposes  to  call  a  beaker,  would  be  just  .01  of  a 
cubic  foot  in  capacity.  And  by  taking  this  as  our  unit  of  capa- 


APPENDIX.  3.17 

city,  our  units  of  length,  of  weight,  and  of  capacity  would  all  be 
connected  decimally.  "And  thus,"  as  Sir  John  Herschel  says, 
"the  change  which  would  place  our  system  of  linear  measure 
on  a  perfectly  faultless  basis,  would  at  the  same  time  rescue 
our  weights  and  our  measures  of  capacity  from  their  present 
utter  confusion,  and  secure  that  other  advantage,  second  only 
in  importance  to  the  former,  of  connecting  them  decimally  with 
that  system  on  a  regular,  intelligible,  and  easily  remembered 
principle,  and  that,  too,  by  an  alteration  practically  imper- 
ceptible in  both  cases,  and  interfering  with  no  one  of  our 
usages  and  denominations." 

These  units  once  established,  they  could  of  course  be  divided 
and  multiplied  decimally  in  the  same  way  as  the  French  units 
are.  If  these  decimal  divisions  and  multiples  were  found  more 
convenient  than  the  old  ones,  they  would  soon  displace  them, 
as  the  decimal  system  in  our  currency  has  displaced  the  old 
system  of  pounds,  shillings,  and  pence. 


V. 

THE  latest  observations  upon  Limit  (according  to  Silliman's 
Journal,  July,  1867),  appear  to  show  in  the  centre  of  the  bright 
spot  covering  the  former  crater  a  minute  black  spot  indicating 
a  crater  of  about  six  hundred  yards  diameter.  The  original 
crater  appears  to  have  been  a  deep  one,  and  about  ten  thousand 
yards  in  diameter.  This  small  crater  was  so  plainly  visible  as 
to  have  been  noticed  (independently  as  it  would  seem)  by  Dr. 
Schmidt  at  Athens,  by  Father  Secchi  at  Rome,  and  by  Pro- 
fessor Lyman  at  New  Haven.  It  was  detected  at  New  Haven 
three  days  after  the  sun  had  risen  over  the  horizon  of  Linnt, 
and  when  the  sun  was  therefore  30°  or  35  °  liigh  upon  it.  These 
observations  show  that  any  change  which  has  taken  place  is 
not  in  the  nature  of  a  development  of  a  cloud,  but  imply  rather 
that  the  old  crater  has  been  filled  up  by  an  eruption  from 
the  small  one  now  visible. 


APPENDIX. 


TABLES. 
THE   SUN  AND   PRINCIPAL   PLANETS. 


0 

Time  of 

Inclination 

Mean     j 

£ 

Name. 

,0 

Axial 

of  Orbit 

Diameter     Volume. 

Mass. 

'2 

cl 

Rotation. 

to  Ecliptic. 

in  Miles. 

o 

h.     m.    s. 

O       1        M 

1 

The  Sun 

e 

600 

887,000  .  1416000 

354936 

0-25 

Mercury 

24    5  28 

708 

2,950  !      0.059 

O.IlS 

2.01 

Venus 

<j> 

23   21    21 

3  23  31 

7,800!      0.912 

0.883 

0.97 

The  Earth 

0 

23  56    4 

7,912  1       i.ooo 

I.OOO 

I.OO 

Mars 

£ 

24  37  22 

i  5i     5 

4,500!      0.183 

0.132 

0.72 

Jupiter 

H 

9  55  26  :  i  18  40 

88,000  1412.000 

338.034 

0.24 

Saturn 

h 

10  29  1712  29  28 

73,000    770.000 

101.064 

0.13 

Uranus 

o  46  30 

36,000  !     95  900 

14.789 

0.15 

Neptune 

W 

i  46  59 

35,000  s     89.500 

24.648 

0.27 

THE    PLANETS  (continue^ 


Relative 

Name. 

Sidereal  Period 
in  Days. 

Relative 
Distance 
from  Sun. 

Mean  Distance  from 
Sun  in  Miles. 

Li^ht  ami 
Heat  re- 
ceived from 

Sun. 

Mercury 

87.969 

0.387 

37,OOO,OOO 

6.67 

Venus 

224.701 

0.723 

69,000,000 

I.9I 

Earth 

365-256 

I.OOO 

95,OOO,OOO 

I.OO 

Mars 

686.980 

1.524 

I45,OOO,OOO 

0-43 

Jupiter 

4,332.585 

5.203 

436,000,000 

0.037 

Saturn 

10.759.220 

9-539 

9O9,OOO,COO 

O.OII 

Uranus 

30,686.821 

19.183 

I,828,OOO,OOO 

0.003 

Neptune 

60,126.722 

30.037 

2,862,OOO,OOO 

O.OOI 

THE  MOON. 

Mean  Distance  from  the  Earth 238,900  miles. 

Sidereal  Period  of  Revolution 27d  7h  43™  11.46'. 

Synodical  Period  of  Revolution 29*    I2h   44™  2.87'. 

Diameter 2160  miles. 

Inclination  of  the  Orbit 5°  8'  48". 

Density  (the  Earth  =  i) 05657. 

Mass  (the  Earth  =  i)    ^. 


APPENDIX. 


319 


THE  MINOR  PLANETS. 


No. 

Name. 

Date  of  Discovery. 

Discoverer. 

Sidereal 
Rev.  in 
Days. 

I 

Ceres  

1  80  1,  Jan.        i 

1680 

2 

Pallas 

1802,  March  28 

Gibers  

1682 

3 

Juno 

1804.    Sent       i 

Harding  . 

icq6 

I 

Vesta 

1807    March  29 

Olbers 

1  726 

c 

Astrcea  

1845,  Dec-       8 

Hencke  

ISI2 

i 

Hebe. 

1847,   July        I 

Hencke.  . 

1  770 

7 

Iris 

1847    Aug     13 

Hind 

M/y 
I  34.6 

8 

Flora 

1847    ^ct       J8 

Hind 

I  IQ7 

q 

Metis  

1848,  April    25 

Graham  .... 

iAyj 

1^4.6 

IO 

Hygieia  

1849,  April    12 

Gasparis  .  . 

2O47 

ii 

Pavthenope 

1850    May     ii 

Luther. 

I4O7 

T- 

Victoria 

1850    Sept     13 

Hind 

1  3O7 

n 

E^eria 

i8co    Nov       2 

Gasparis 

»5VJ 

I  C.  1  1 

14 

Irene  

1851,  May     19 

Hind  

1  J1  1 

I  s  IQ 

1C 

Eunomia 

l8sl      Tlllv       2Q 

Gasparis  . 

I  ^7O 

16 

Psvche 

1852    March  1  7 

Gasparis 

1  D/v 
l828 

17 

Thetis  

1852,  April    17 

Luther  

1  42  1 

18 

Melpomene  .  .  . 

1852,  June    24 

Hind  .  .  . 

1271 

IQ 

Fortuna  

1832    Aug     22 

Hind  .  .  . 

1  7Q7 

2O 

Massilia  

1852,  Sept.    19 

Gasparis  

16V6 
IT.OS 

21 

Lutetia  

1852,  Nov.    15 

Goldschmidt 

1388 

22 

Calliope  

1852,  Nov.    16 

Hind  . 

1817 

2"? 

Thalia  

1852,  Dec.     15 

Hind  

jcc6 

24 

Themis  

18^1,  April     ? 

Gasparis  

IDD" 
2O7O 

25 

Phocaea  

18^.  April     7 

Chacornac  . 

I7C8 

26 

Proserpine  .... 

1857,  May       5 

Luther  

ii;  80 

27 

Euterpe  

1853    Nov       8 

Hind 

28 

Uellona  

1854,  March    I 

Luther 

J  j1  j 
1692 

29 

Amphitrite.  .  .  . 

1854,  March    I 

Marth  

1  4.Q2 

•JQ 

Urania  

l8?4,    Tulv       22 

Hind 

71 

Euphrosyne  .  .  . 

1854,  Sept.      i 

Ferguson 

£j^y 
2048 

72 

Pomona  

1854,  Oct.     26 

Goldschmidt 

r  C2I 

33 

-24 

Polyhymnia  .  .  . 
Circe  

1854,  Oct.     28 
1855,  April     6 

Chacornac  

1^1 
1778 

35 

Eeucothea  .... 

1855,  April    19 

Luther  

iuuy 

IQO7 

36 

Atalanta  

18^,  Oct.       c 

Goldschmidt 

1664 

VJ 

Fides  

i8cc,  Oct        c 

Luther 

38 

Lecla  

i8c6    Jan       12 

ijuy 

70 

Lsetitia  

1856,  Feb.       8 

Chacornac 

lvb7 
1684 

40 
4-1 

Harmonia     .  .  . 
Daphne  

1856,  March  3  1 
1856,  May     22 

Goldschmidt  

1247 

1681 

42 

Isis  

18^6,  May     27 

Pogson 

I  7Q2 

43 

Ariadne  

1857,   April    15 

Pogson  

I  iqc 

44 

Nysa 

i8c7    Mav     27 

45 

Eugenia  

18^7    Tune    27 

'379 
1678 

46 

Hestia  

1857,  Aug.     16 

Po°"son 

I4.7O 

48 

Melete*...... 
Aglaia  

1857,  Sept.      9 
1857,  Sept.    15 

Goldschmidt  
Luther  

1529 

1788 

*  Goldschmidt  at  first  believed  it  to  be  Daphne  (41),  but,  finding  its  period  differ- 
ent, called  it  Pseudo-Daphne.  It  was  not  seen  from  1857  to  1861,  when  Schubert 
rediscovered  it  and  named  it  Melete. 


320 


APPENDIX. 


No. 

Name. 

Date  of  Discovery. 

Discoverer. 

Sidereal 
Rev.  in 
Days. 

49 

Doris  

18^7,  Sept.    IQ 

Goldschmidt 

2OO7 

CQ 

Pales  

i8c.7.  Sent     IQ 

Goldschmidt 

TQ7C 

CI 

Virginia  

18^,7,  Oct.       4 

Ferguson  

^y/j 
i  ^76 

C2 

Nemausa  

1858,  Jan.      22 

Laurent.    . 

1778 

C7 

Europa  

1858,  Feb        6 

Goidschmidt 

ijj° 

CA 

Calvpso  

1858,  April     4 

Luther  

xyyj 
i^A8 

t;S 

Alexandra  

1858,  Sept.    10 

Goldschmidt  

1674 

5* 

Pandora  

1858,  Sept.    10 

Searle  

•"OT1 

l6?d. 

C7 

Mnemosyne  .  .  . 

1859,  Sept.    22 

Luther 

2O  AQ 

58 

Concordia  .... 

1860,  March  24 

Luther  

161  c. 

cq 

Danae  

i  860    Sept      9 

60 

Olympia  (Elpis) 

1860,  Sept.    12 

Chacornac 

l67A 

6r 

Erato  

1860    Sept     14 

Forster 

2O2"1 

62" 

Echo         .... 

1860    Sept     1  1» 

63 

Ausonia  

1  86  1,  Feb.     10 

Gasparis 

1OJ^ 
I  7  C  C 

64 

Angelina  

1  86  1,  March  4 

Tempel  

I6bb 
1601 

*5 

Cybele  

1  86  1,  March   8 

Tern  pel  .  . 

2711 

66 

1861    April     9 

Tuttle 

1588 

67 

Asia  

1  86  1    April    17 

I  °7C 

68 

Hesperia 

1861    April   29 

1J/J 
1807 

69 

Leto  

1  86  1    April  29 

Luther 

ioyj 
1601 

7o 

Panopea  . 

1861    May       5 

Goldschmidt 

I  CA2 

71 

Feronia 

1861    May     29 

*M* 

72 

Niobe  .    .    . 

1861    Aucr.    1  1 

Luther 

*245 
1671 

73 

Clytie  

1862,  April     7 

Tuttle  . 

ICQO 

74 

Galatea  

1862    Aug     29 

Tempel 

1691 

75 

Eurydice  

1862,  Sept.   22 

Peters  

ICQ4 

76 

Freia  

1862,  Oct.     21 

d'Arrest  . 

2080 

77 

Frierera.  . 

1862    Nov     12 

Peters 

I  ^06 

78 

Diana  

1863,  March  15 

Luther.  .  .  . 

ICC4 

70 

Eurynome  .... 

1867.  Sept.    14 

Watson 

1  7QO 

80 

Sappho  . 

1864    May       2 

Pogson 

I27O 

81 

Terpsichore  .  .  . 

1864,  Sept.   30 

Tempel  

1607 

8^ 

Alcmene  

1864    Nov     27 

Luther.  . 

1  6  CQ 

8-? 

Keatrix  . 

186^    April  26 

Gasparis 

1781 

84 

Clio  

1865    Aug.    26 

Luther  

1J01 

I77Q 

85 

Jo  

1865    Sept.    19 

Peters  .  . 

jc87 

86 

Semele  . 

1866    Jan        4 

Tietjen 

IQ87 

87 

Sylvia  

1866    May     1  6 

Pogson  

2784 

88 

Thisbe  

1866    June    15 

Peters  .  .  . 

j67C 

80 

Julia  

1866,  Aug.      6 

Stephan  

1472 

9° 

Antiope  

1866,  Oct.      ii 

Luther  

2O7I 

01 

1866    Nov       4 

Stephan 

Q2 

Undina  ... 

186?    Tulv       7 

Peters 

2086 

07 

1867,  Aucr.    24 

Watson 

1669 

Q4 

1867    Sept      6 

Watson 

(»S 

1867,  Nov.    23 

Luther.  .  .  . 

p 

I 
APPENDIX.  321 

The  numerical  order  of  the  minor  planets  differs  some- 
what in  the  lists  of  English  and  French  astronomers. 

Of  the  first  eighty-nine  of  these  planets,  the  nearest  to  the 
sun  is  Flora,  whose  mean  distance  is  201,274,000  miles. 

The  farthest  from  the  sun  is  Sylvia,  with  a  mean  distance  of 
about  319,500,000  miles. 

The  least  eccentric  orbit  is  that  of  Europa,  which  is  even 
nearer  to  an  exact  circle  than  the  orbit  of  Venus.  The  most 
eccentric  orbit  is  that  of  Polyhymnia,  whose  aphelion  distance 
is  rather  more  than  double  its  perihelion  distance. 

The  orbit  of  Massilia  has  the  least  inclination  to  the  eclip- 
tic, or  o°  41' ;  that  of  Pallas  the  greatest  inclination,  or  34°  42'. 

The  brightest  planet  is  Vesta,  which  appears  at  times  as  a 
star  of  the  sixth  magnitude.  The  faintest  is  Atalanta,  which, 
under  the  most  favorable  circumstances,  is  scarcely  above  the 
thirteenth  magnitude. 

The  largest  planet,  according  to  some  authorities,  is  Pallas. 
Lament  makes  its  diameter  670  miles,  but  Galle  only  172  miles. 
According  to  others,  Vesta  is  the  largest,  with  a  diameter  of  228 
miles.  The  more  recently  discovered  planets  are  all  so  small 
that  it  is  impossible  to  tell  which  is  smallest.  The  diameters 
of  those  numbered  5  -  39,  as  given  by  Chambers,  range  from 
12  miles  (Eunomid)  up  to  in  miles  (Hygieid). 

Of  these  planets  (up  to  the  ninety-fourth  inclusive),  fifteen 
have  been  discovered  in  the  United  States,  —  Euphrosyne,  Vir- 
ginia, Pandora,  Echo,  Maia,  Feronia,  Clytie,  Eurydice,  Frigga, 
Eurynome,  lo,  Thisbe,  and  Undina,  with  the  93d  and  94th,  which 
are  not  yet  (January,  1868)  named. 

In  several  cases  minor  planets  have  been  discovered  inde- 
pendently by  two  or  more  observers,  each  knowing  nothing  of 
what  the  other  had  done.  Thus,  Irene  'was  discovered  by 
Hind,  May  19,  1851,  and  by  Gasparis,  May  23;  Massilia,  by 
Gasparis,  September  19,  1852,  and  by  Chacornac,  September 
20;  Amphitrite,  by  Marth,  March  I,  1854,  by  Pogson,  March  2, 
and  by  Chacornac,  March  3. 


14* 


322 


APPENDIX. 


MOONS   OF  JUPITER. 


Moon. 

Sidereal  Period 
of  Revolution. 

Distance  in  Radii 
of  Jupiter. 

Mean  Distance 
in  Miles. 

I. 

d.       h.      in. 
I      18     28 

6.049 

278,542 

II. 

3      13      IS 

9.623 

442,904 

III. 
IV. 

7      3    43 
16    16    32 

I5-350 
26.998 

706,714 
I,20O,OOO 

MOONS   OF  SATURN. 


Moon. 

Sidereal  Period 
of  Revolution. 

Distance  in  Radii 
of  Saturn. 

Mean  Distance 
in  Miles. 

I. 

d.      h.      m. 
0     22     36 

3-36I 

Il8,COO 

II. 
III. 

I        8     58 
I      21      18 

4.313 
5-340 

152,000 
188,000 

IV. 

2      17      41 

6.840 

240,000 

V. 

4     12    25 

9-553 

336,000 

VI. 

.15      22      41 

22.145 

778,000 

VII. 

21       12        0 

28.000 

94O,COO 

VIII. 

.79      7    55 

64-359 

2,268,OCO 

MOONS   OF  URANUS. 


Moon. 

Sidereal  Period 
of  Revolution. 

Distance  in  Radii 
of  Uranus. 

Mean  Distance 
in  Miles. 

I. 

d.      h.      m. 
2      12      17 

6.940 

119,994 

II. 
III. 
IV. 

4      3    28 
8     16    56 
13     ii      7 

9.720 
15.890 
2I.27O 

170,863 
288,600 
380,000 

MOON   OF  NEPTUNE. 

Sidereal  Period  of  Revolution 5*  2Oh  5om  45s. 

Mean  Distance  from  Neptune 236,000  miles. 


APPENDIX.  323 


THE  CONSTELLATIONS. 

1.  ALL  the  stars  in   the  heavens  have  been  divided  into 
groups  called  constellations  (162).     Many  of  these  were  recog- 
nized and  named  at  a  very  early  period  ;  and  some  of  them,  as 
Orion,  are  mentioned  in  the  Old  Testament. 

The  method  of  naming  the  stars  in  each  constellation  has 
been  explained  above  (163).  The  characters  and  names  of  the 
Greek  alphabet  are  as  follows  :  — 

a,  Alpha.  v,  Nu. 

0,  Beta.  £,  Xi. 

y,  Gamma.  o,  Omicron. 

8,  Delta.  IT,  Pi- 

€,  Epsilon.  p,  Rho. 

£,  Zeta.  <r,  Sigma. 

rj,  Eta.  r,  Tau. 

0,  Theta.  u,  Upsilon. 

1,  Iota.  <£,  Phi. 
K,  Kappa.  x,  Chi. 
A,  Lambda.  ^,  Psi. 

p,        Mu.  o>,        Omega. 

If  a  constellation  has  more  stars  than  can  be  named  from  the 
Greek  alphabet,  the  Roman  alphabet  is  used  in  the  same  way ; 
and  when  both  alphabets  are  exhausted,  numbers  are  used. 

2.  Circumpolar  Constellations.  —  One  of  the  most  important 
constellations,  and  one  easily  recognized,  is  the  Great  Bear,  or 
Ursa  Major.     It  is  represented  in  Plate  I.  at  the  end  of  this 
volume.     It  may  be  known  by  the  seven  stars  forming   "the 
Dipper,"    or   "  Charles's   Wain,"   as  it  is*  sometimes    called. 
These  stars  are  designated  by  the  first  seven  letters  of  the 
Greek  alphabet ;  and  the  name  and  position   of  each  should  be 
carefully  fixed  in  the  mind,  as  we  shall  have  frequent  occasion 
to  refer  to  them.     The  Bear's  feet  are  marked  by  three  pairs  of 
stars.     These  and  the  star  in  the  nose  can  be  readily  found  by 
means  of  the   lines  drawn  on  the  chart.     It  may  be  remarked 
here,  that  in  all  cases  the  stars  thus  connected  by  lines  are  the 
leading  stars  of  the  constellation,  and  should  be  thoroughly 


324  APPENDIX. 

learned.  The  stars  a  and  £  are  called  the  Pointers.  If  a  line 
be  drawn  from  /3  to  a,  and  prolonged  about  five  times  the  dis- 
tance between  them,  it  will  pass  near  an  isolated  star  of  the  sec- 
ond magnitude  known  as  the  Pole  Star,  or  Polaris.  This  is 
the  brightest  star  in  the  Little  Bear,  or  Ursa  Minor  (Plate  II.). 
It  is  in  the  end  of  the  handle  of  a  second  and  smaller  "dip- 
per." The  stars  /3  and  y  of  this  constellation  are  quite  bright, 
and  are  nearly  parallel  with  e  and  £  of  the  other  Bear. 

On  the  opposite  side  of  the  Pole  Star  from  the  Great  Bear, 
and  at  about  the  same  distance,  is  another  conspicuous  constel- 
lation, called  Cassiopeia.  Its  five  brightest  stars  form  an  irreg- 
ular W,  opening  towards  the  Pole  Star  (Plate  II.). 

About  half-way  between  the  two  Dippers  three  stars  of  the 
third  magnitude  will  be  seen,  —  the  only  stars  at  all  prominent 
in  that  neighborhood.  These  belong  to  Draco,  or  the  Dragon. 
The  chart  will  show  that  the  other  stars  in  the  body  of  the 
monster  form  an  irregular  curve  around  the  Little  Bear,  while 
the  head  is  marked  by  four  stars  arranged  in  a  trapezium. 
Two  of  these  stars,  £  and  y,  are  quite  bright.  A  little  less  than 
half-way  from  Cassiopeia  to  the  head  of  the  Dragon  is  the  con- 
stellation Cepheus,  five  stars  of  which  form  an  irregular  K. 

These  five  constellations  never  set  in  our  latitude,  and  are 
called  circttmpolar  constellations  (page  5). 

3.  Constellations  visible  in  September.  —  We  will  now  study 
the  remaining  constellations  visible  in  our  latitude,  beginning 
with  those  which  are  above  the  horizon  at  eight  o'clock  in  the 
evening,  about  the  middle  of  September.  At  this  time  the 
Great  Bear  will  be  low  down  in  the  northwest,  and  the  Drag- 
on's head  nearly  in  the  zenith.  If  we  draw  a  line  from  £  to  T;  of 
the  Great  Bear  and  prolong  it,  we  shall  find  that  it  will  pass 
near  a  reddish  star  of  the  first  magnitude.  This  star  is  called 
Arcturns,  or  a  Bootis,  since  it  is  the  brightest  star  in  the  con- 
stellation Bootes.  Of  its  other  conspicuous  stars,  four  form  a 
cross.  These  and  the  remaining  stars  of  the  constellation  can 
be  readily  traced  with  the  aid  of  Plate  III. 

Near  the  Dragon's  head  (Plate  IV.)  maybe  seen  a  very  bright 
star  of  the  first  magnitude,  shining  with  a  pure  white  light. 
This  star  is  Vega,  or  a  Lyres.  Of  this  and  some  of  the  other 
stars  in  the  Lyre  we  shall  have  occasion  to  speak  hereafter. 


APPENDIX.  325 

If  we  draw  a  line  from  Arcturus  to  Vega  (Plate  III.)i  it  will 
pass  through  two  constellations,  —  the  Crown,  or  Corona  Bore- 
alts,  and  Hercules.  The  former  is  about  one  third  of  the  way 
from  Arcturus  to  Vega,  and  consists  of  a  semicircle  of  six  stars, 
the  brightest  of  which  is  called  Alphecca,  or  Gemma  Coroncs,  — 
the  gem  of  the  Crown. 

Hercules  is  about  half-way  between  the  Crown  and  Vega. 
This  constellation  is  marked  by  a  trapezoid  of  stars  of  the  third 
magnitude.  A  star  in  one  foot  is  near  the  Dragon's  head  ;  there 
is  also  a  star  in  each  shoulder,  and  one  in  the  face. 

Just  across  the  Milky  Way  from  Vega  (Plate  V.)  is  a  star  of 
the  first  magnitude,  called  Altair  or  a  Aquilce.  This  star  marks 
the  constellation  Aquila,  or  the  Eagle,  and  may  be  recognized 
by  a  small  star  on  each  side  of  it.  These  are  the  only  important 
stars  in  this  constellation. 

In  the  Milky  Way,  between  Altair  and  Cassiopeia  (Plate  IV.), 
there  is  a  large  constellation  called  Cygnus,  or  the  Swan.  Six 
of  its  stars  form  a  large  cross,  by  which  it  will  be  readily  known. 
a  Cygni  is  often  called  Deneb.  It  forms  a  large  isosceles  tri- 
angle with  Altair  and  Vega. 

Low  down  in  the  south,  on  the  edge  of  the  Milky  Way  (Plate 
VI.),  is  a  constellation  called  Sagittarius,  or  the  Archer.  It  may 
be  known  by  five  stars  forming  an  inverted  dipper,  often  called 
"the  Milk-dipper."  The  head  is  marked  by  a  small  triangle. 
The  other  stars,  as  seen  by  the  map,  may  be  grouped  so  as  to 
represent  a  bow  and  an  arrow. 

Low  in  the  southwest  is  a  bright  red  star  called  Antares,  or 
a  Scorpionis.  This  constellation  is  described  below  (12). 

The  space  between  Sagittarius  and  Hercules  and  Scorpio  is 
occupied  by  the  Serpent  (Serpens]  and  the  Serpent-bearer,  or 
Ophiuchus  (Plates  VI.  and  VII.).  The  head  of  the  Serpent  is 
near  the  Crown,  and  marked  by  a  small  triangle.  The  head  of 
Ophiuchus  is  close  to  the  head  of  Hercules,  and  may  be  known 
by  a  star  of  the  second  magnitude.  Each  shoulder  is  marked 
by  a  pair  of  stars.  His  feet  are  near  the  Scorpion.  The  Ser- 
pent can  be  best  traced  with  the  aid  of  the  map. 

Nearly  on  a  line  with  Arcturus  and  y  Ursae  Majoris  (Plate  I.), 
and  rather  nearer  the  latter,  is  an  isolated  star  of  the  third  mag- 
nitude, called  Cor  Caroli,  or  Charles's  Heart.  This  is  the  only 


326  APPENDIX. 

prominent  star  in  the  constellation  of  Canes  Venatici,  or  the 
Him  ting  Dogs. 

Cassiopeia  is  almost  due  east  of  the  Pole  Star.  A  line 
drawn  from  the  latter  through  £  Cassiopeiae,  and  prolonged, 
passes  through  two  stars  of  the  second  and  third  magnitude. 
These,  with  two  others  farther  to  the  south,  form  a  large 
square,  called  the  Square  of  Pegasus.  Three  of  these,  as  seen 
by  the  map  (Plate  V.),  belong  to  the  constellation  Pegasus,  or 
the  Winged  Horse,  a.  Pegasi  is  called  Markab,  and  /3  is  called 
Algenib.  The  bright  stars  in  the  neck  and  nose  can  be  found 
by  the  map. 

The  fourth  star  in  the  Square  of  Pegasus  belongs  (Plate  VIII.) 
to  the  constellation  Andromeda.  Nearly  in  a  line  with  a  Pegasi 
and  this  star  are  two  other  bright  stars  belonging  to  Androm- 
eda. The  stars  in  her  belt  may  be  found  by  the  map. 

Following  the  direction  of  the  line  of  stars  in  Andromeda  just 
mentioned,  and  bending  a  little  towards  the  east,  we  come  to 
Algol,  or  /3  Persei,  a  remarkable  variable  star  (165).  This  star 
may  be  readily  recognized  from  the  fact  that,  together  with  £ 
and  y  Andromedae  and  the  four  stars  in  the  Square  of  Pegasus, 
it  forms  a  figure  similar  in  outline  to  the  Dipper  in  Ursa  Major, 
but  much  larger.  If  the  handle  of  this  great  Dipper  is  made 
straight  instead  of  being  bent,  the  star  in  the  end  of  it  is  a  Per- 
sei, of  the  second  magnitude.  This  star  has  one  of  the  third 
magnitude  on  each  side  of  it.  The  other  stars  in  Perseus  may 
be  found  by  the  chart. 

Just  below  6  in  the  head  of  Pegasus  (Plate  IX.)  are  three  stars 
of  the  third  and  fourth  magnitudes,  forming  a  small  arc.  These 
mark  the  urn  of  Aquarius,  the  Water-bearer.  His  body  con- 
sists of  a  trapezium  of  four  stars  of  the  third  and  fourth  magni- 
tudes. Small  clusters  of  stars  show  the  course  of  the  water 
flowing  from  his  urn. 

This  stream  enters  the  mouth  of  the  Southern  Fish,  or  Piscis 
Australis.  The  only  bright  star  in  this  constellation  is  Fomal- 
haut,  which  is  of  the  first  magnitude,  and  at  this  time  will  be 
low  down  in  the  southeast. 

To  the  south  of  Aquarius  is  Capricornus,  or  the  Goat.  He 
is  marked  by  three  pairs  of  stars  arranged  in  a  triangle.  One 
pair  is  in  his  head,  another  in  his  tail,  and  the  third  in  his  knees. 


APPENDIX.  327 

Near  Altair  (Plate  V.),  and  a  little  higher  up,  is  a  small-dia- 
mond of  stars  forming  the  Dolphin,  or  Delphinus. 

A  little  to  the  west  of  the  Dolphin,  in  the  Milky  Way,  are  four 
stars  of  the  fourth  magnitude,  which  form  the  constellation  Sa- 
gitta,  or  the  Arrow. 

4.  Constellations  visible  in   October.  —  If   we  look  at  the 
heavens  at  £ight  o'clock  on  the  I5th  of  October,  we  shall  see 
that  all  the  constellations  described  above  have  shifted  some- 
what towards  the  west.    Arcturus  and  Antares  have  set.     In  the 
east,  below  Andromeda  (Plate  X.),  we  see  a  pair  of  bright  stars, 
which  are  the  only  conspicuous  ones  in  Aries,  or  the  Ram. 

About  half-way  between  Aries  and  y  Andromedae  are  three 
stars  which  form  a  small  triangle.  This  constellation  is  called 
Triangulum,  or  the  Triangle. 

Between  Aries  and  Pegasus  is  the  constellation  Pisces,  or  the 
Fishes.  The  southernmost  Fish  may  be  recognized  by  a  penta- 
gon of  small  stars  lying  below  the  back  of  Pegasus.  There  are 
no  conspicuous  stars  in  the  other  Fish,  which  is  directly  below 
Andromeda.  The  stars  in  the  band  connecting  the  Fishes  may 
be  traced  with  the  help  of  the  map. 

5.  Constellations  visible  in  November.  —  At  eight  o'clock  in 
the  evening  on  the  15th  of  November,  we  see  at  a  glance  that 
the  constellations  with  which  we  have  become  acquainted  have 
moved  yet  farther  to  the  westward.     Bootes,  the  Crown,  Ophi- 
uchus,  and  the  Archer  have  set ;     Pegasus,  Cassiopeia,  and 
Andromeda  are  overhead  ;  while  new  constellations  appear  in 
the  east. 

We  notice  at  once  (Plate  XL)  a  very  bright  star  in  the  north- 
east, directly  below  Perseus.  This  is  Capella,  or  a  Auriga. 
There  are  five  other  conspicuous  stars  in  Auriga,  or  the  Chari- 
oteer; and  with  Capella  they  form  an  irregular  pentagon. 

Somewhat  to  the  eastward  (Plate  XII.),  and  a  little  lower 
down,  is  a  very  bright  red  star.  This  is  Aldebaran,  or  a  Tauri. 
It  is  familiarly  known  as  the  Bull's  eye.  It  will  be  noticed  by 
the  map  that  it  is  at  one  end  of  a  V  which  forms  the  face  of  the 
Bull.  This  group  is  known  as  the  Hyades.  Somewhat  above 
the  Hyades  is  a  smaller  group,  called  the  Pleiades,  —  more  com- 
monly known  as  the  Seven  Stars,  though  few  persons  can  dis- 
tinguish more  than  six.  The  bright  star  on  the  northern  horn, 


328  APPENDIX. 

or  /3  Tauri,  is  also  in  the  foot  of  Auriga,  and  counts  as  y  of  that 
constellation. 

All  the  space  between  Taurus  and  the  Southern  Fish,  and 
below  Aries  and  Pisces  (Plate  XIII.),  is  occupied  by  Cetus,  the 
Whale.  The  head  is  marked  by  a  triangle  of  rather  conspicu- 
ous stars  below  Aries  ;  the  tail,  by  a  bright  star  of  the  second 
magnitude,  which  is  now  just  about  as  far  above  the  horizon  as 
Fomalhaut.  On  the  body  are  five  stars,  forming  a  sort  of  sickle. 
About  half-way  between  this  sickle  and  the  triangle,  in  the  head, 
is  o  Ceti,  also  called  Mira,  or  the  wonderful  star  (165). 

6.  Constellations  visible  in  December.  —  At  eight  o'clock  in 
the  evening  in  the  middle  of  December,  we  shall  find  that  Her- 
cules, Aquila,  and  Capricornus  have  sunk  below  the  horizon  ; 
while  Vega  and  the  Swan  are  on  the  point  of  setting.     The 
Great  Bear  is  climbing  up  in  the  northeast.     In  the  east  we  be- 
hold by  far  the  most  brilliant  group  of  constellations  we  have 
yet  seen.     Capella  and  Aldebaran  are  now  high  up  ;  and  below 
the  former  (Plate  XII.)  is  the  splendid  constellation  of  Orion. 
His  beltt  made  up  of  three  stars  in  a  straight  line,  will  be  recog- 
nized at  once.    Above  this,  on  one  shoulder,  is  a  star  of  the  first 
magnitude,  called  Betelgeuse,  or  a  Orionis.     About  as  far  from 
the  belt,  on  the  other  side,  is  another  star  of  the  first  magnitude, 
called  Rigel.     There  are  two  other  fainter  stars  which  form  a 
large  trapezium  with  Betelgeuse  and  Rigel.     The  three  small 
stars  below  the  belt  are  upon  the  sword. 

Below  Orion  (Plate  XIV.)  is  a  small  trapezium  of  stars  which 
are  in  the  constellation  of  Lepus,  or  the  Hare.  The  head  is 
marked  by  a  small  triangle,  as  seen  on  the  map. 

To  the  north  of  Orion,  and  a  little  lower  down  (Plate  XII.), 
are  two  bright  stars  near  together,  one  of  the  first  and  the  other 
of  the  second  magnitude.  The  latter  is  caJled  Castor,  and  the 
former  Pollux.  They  are  in  the  constellation  Gemini,  or  the 
Twins.  A  line  of  three  smaller  stars  just  in  the  edge  of  the 
Milky  Way  marks  the  feet,  and  another  line  of  three  the  knees. 
Pollux  forms  a  large  triangle  with  Capella  and  Betelgeuse. 

7.  Constellations  visible  in  January.  —  At  eight  in  the  even- 
ing on  the  1 5th  of  January,  Vega,  Altair,  the  Dolphin,  Aquarius 
and  Fomalhaut  have  disappeared  in  the  west ;  Deneb  and  the 
Square  of  Pegasus  are  near  the  horizon  j  while   Capella  and 


APPENDIX.  329 

Aldebaran  are  nearly  overhead.  Two  stars  of  exceeding  bril- 
liancy have  come,  up  in  the  west.  The  one  farthest  to  the 
south  (Plate  XIV.)  is  the  brightest  star  in  the  whole  heavens. 
It  is  called  Sirius,  or  the  Dog-star ;  and  is  in  the  constellation 
of  Cam's  Major,  or  the  Great  Dog,  which  can  be  readily  traced 
by  the  lines  on  the  map. 

The  other  bright  star  is  between  Sirius  and  Pollux  (Plate 
XII.),  and  is  called  Procyon.  It  is  in  Cam's  Minor,  or  the  Lit- 
tle Dog.  The  only  other  prominent  star  in  this  constellation  is 
one  of  the  third  magnitude  near  Procyon. 

Procyon,  Sirius,  and  Betelgeuse  form  a  large  equilateral 
triangle. 

Orion  and  the  group  of  constellations  about  it  constitute  by 
far  the  most  brilliant  portion  of  the  heavens,  as  seen  in  our  lat- 
itude. There  are,  in  all,  but  about  twenty  stars  of  the  first  mag- 
nitude, and  seven  of  these  are  in  this  immediate  vicinity. 

8.  Constellations  visible  in  February.  —  If  we  look   at  the 
heavens  at  the  same  time  in  the  evening  about  the  middle  of 
February,  we  shall  miss  Cygnus  and  Pegasus  from  the  west. 
Auriga  and  Orion  are  nearly  overhead. 

Southeast  of  the  Great  Bear  (Plate  XV.)  is  a  red  star  of  the 
first  magnitude,  called  Regulus,  in  the  constellation  of  Leo,  or 
the  Lion.  There  are  five  stars  near  Regulus,  which  together 
with  it  form  a  group  often  called  the  Sickle.  The  star  in  the 
tail  is  Denebola,  which  makes  a  right-angled  triangle  with  two 
others  near  it. 

Between  Leo  and  Gemini  is  the  constellation  Cancer,  or  the 
Crab.  It  contains  no  bright  stars,  but  a  remarkable  cluster  of 
small  stars  called  Prasepe,  or  sometimes  the  Beehive. 

Below  Regulus  (Plate  XIV.)  is  a  bright  red  star  of  the  second 
magnitude,  called  Cor  Hydra,  or  the  Hydra's  Heart.  The  head 
of  Hydra  is  marked  by  five  small  stars.  The  coils  of  the  mon- 
ster can  be  traced  by  the  map.  A  portion  of  the  constellation 
is  on  Plate  XVI. 

9.  Constellations   visible  in  March.  —  At    the    middle    of 
March,  the  heavens  will  have  shifted  round  somewhat  towards 
the  west ;  but  all  the  conspicuous  constellations  of  the  preced- 
ing month  are  still  visible,  while  no  new  ones  at  all  brilliant 
have  come  into  view. 


330  APPENDIX. 

If  we  draw  a  line  from  the  end  of  the  Great  Bear's  tail  to 
Denebola,  it  will  pass  through  two  constellations,  —  Canes  Ve- 
natici,  mentioned  above  ;  and  Coma  Berenices,  or  Berenice's 
Hair,  a  large  cluster  of  faint  stars  (Plate  XV.). 

10.  Constellations  "visible  in  April.  —  At  the  middle  of  April, 
Aries  and  Andromeda  have  set ;    Taurus,   Orion,  and   Canis 
Major  are  sinking  towards  the  west ;  the  Great  Bear  and  the 
Lion  are  overhead  ;  Arcturus  has  risen  in  the  northeast  (Plate 
XVI.) ;  and  some  way  to  the  south  of  this  is  seen  a  star  of  the 
first  magnitude,  which  forms  a  large  triangle  with  Arcturus  and 
Denebola.     It  is  called  Spica  Virginis,  and  is  the  chief  star  in 
the  constellation  Virgo,  or  the  Virgin.    The  stars  on  the  breast 
and  wings  can  be  found  with  the  aid  of  the  map. 

South  of  Virgo  is  a  trapezium  of  four  stars,  which  are  in  the 
constellation  of  Corvus,  or  the  Crow. 

11.  Constellations  "visible  in  May.  —  At  the  middle  of  May, 
Taurus,  Orion,  and  Canis  Major  have  set ;  Vega  has  just  come 
up  in  the  northeast ;  and  between  Vega  and  Arcturus  we  again 
see  Hercules  and  Corona.     Below  Spica  are  two  stars  of  the 
second  magnitude,  belonging  to  the  constellation  Libra,  or  the 
Balance.     A   star  of  the   fourth   magnitude  forms  a  triangle 
with  these,  and  marks  one  pan  of  the  balance  (Plate  VII.). 

12.  Constellations  visible  in  June.—\n.  June  we  shall  find 
that  Canis  Minor,  Perseus,  Auriga,  and  Gemini  have  either  set, 
or  are  on  the  point  of  setting  ;  Arcturus  is  overhead;  Cygnus 
and  Aquila  are  just  rising.     Ophiuchus  is  well  up  ;  and  low  in 
the  southeast  we  see  again  the  red  star  Antares,  in  the  constel- 
lation Scorpio,  or  the  Scorpion  (Plate  VI.).     There  is  a  star  of 
the  third  magnitude  on  each  side  of  Antares,  and  several  stars 
of  the  third  and  fourth  magnitudes  in  the  head  and  claws.    The 
configuration  of  these  stars  is  much  like  a  boy's  kite  with  a  long 
tail.     Scorpio  is  a  very  brilliant  constellation,  and  is  seen  to  bet- 
ter advantage  in  July  and  August. 

13.  Constellations  visible  in  July  and  August.  —  We  have 
now  described  all  the  important  constellations  visible  in  our  lat- 
itude.    Those  which  are  seen  in  July  and  August  are  mainly 
those  described  under  the  last  two  or  three  months,  and  under 
September. 

14.  Southern    Circumpolar    Constellations.  —  There   are   a 


APPENDIX. 


331 


number  of  constellations  near  the  South  Pole  of  the  heavens 
which  never  rise  in  our  latitude,  just  as  there  are  some  near 
the  North  Pole  which  never  set.  These  are  called  the  soiith- 
ern  circumpolar  constellations ,  and  are  shown  in  Plate  XVII. 


CONSTELLATIONS   VISIBLE   EACH   MONTH. 

ffi^^  THE  following  table  gives  the  constellations  visible  at  8  o'clock  in  the  even- 
ing, about  the  middle  of  each  month.  The  stars  opposite  the  names  of  the  constel- 
lations indicate  those  visible  in  the  month  designated  at  the  top. 


Name  of 
Constellation. 

ex 
<u 
C/2 

o 

o 

g 

6 

S 

1 

A 

& 

N 

"C 

ex 

< 

t^, 

rt 

^ 

<u 

3 
>—  » 

>-, 

"3 

*> 

< 

Bootes 

* 

* 

* 

* 

* 

Corona  Borealis 

* 

* 

* 

* 

* 

Ophiuchus 

* 

* 

Sagittarius 

* 

\ 

Hercules 

* 

* 

* 

Lyra 

* 

* 

* 

Aquila 

* 

Delphinus 

* 

Capricornus 

* 

Cygnus 

# 

* 

* 

* 

Sagitta 

* 

* 

Aquarius 

* 

* 

Piscis  Australis 

* 

* 

Pegasus 

* 

* 

Andromeda 

* 

* 

* 

* 

Perseus 

# 

* 

* 

• 

# 

Aries 

* 

# 

* 

Pisces 

* 

Cetus 

* 

* 

Triangulum 

* 

* 

# 

* 

Auriga 

* 

* 

# 

* 

* 

* 

* 

Taurus 

Lepus 

* 

* 

* 

Orion 

*  • 

* 

# 

* 

Gemini 

# 

* 

* 

« 

* 

Canis  Major 

# 

* 

* 

"      Minor 

# 

# 

* 

* 

Cancer 

* 

* 

* 

* 

Hydra 

* 

* 

# 

* 

Leo 

* 

* 

* 

* 

* 

Coma  Berenices 

* 

* 

* 

* 

* 

* 

Canes  Venatici 

Virgo 

* 

* 

*- 

* 

* 

Corvus 

* 

* 

* 

* 

Libra 

* 

* 

* 

* 

Scorpio 

* 

* 

* 

332  APPENDIX. 

The  following  are  the  circiunpolar  constellations  which  are 
visible  all  the  year  round:  Ursa  Major,  Ursa  Minor,  Draco, 
Cassiopeia,  and  Cepheus. 


STARS   OF   THE   FIRST   MAGNITUDE. 

THE  following  is  a  list  of  the  stars  of  the  first  magnitude,  in 
the  order  of  their  brightness  :  — 


1.  Sirius,  or  a  Canis  Majoris. 

2.  17  Argus  ((variable}. 

3.  Canopus,  or  a  Argus. 

4.  a  Centauri. 

5.  Arcturus,  or  a  Bootis. 

6.  Rigel,  or  /?  Orionis. 

7.  Capella,  or  a  Aurigae. 

8.  Vega,  or  a  Lyrae. 

9.  Procyon,  or  a  CanisJVlinoris. 
10.  Betelgeuse,  or  a  Orionis. 


11.  Achernar,  or  a  Eridani. 

12.  Aldebaran,  or  a  Tauri. 

13.  (t  Centauri. 

14.  a  Crucis. 

15.  Antares,  or  u  Scorpionis. 

16.  Altair,  or  a  Aquilae. 

17.  Spica,  or  a  Virginis. 

1 8.  Fomalhaut,  or  a  Piscis  Australis. 

19.  /?  Crucis. 

20.  Pollux,  or  /*  Geminorum. 


Some  astronomers  admit  into  this  class  only  the  first  sev- 
enteen of  the  above  list.  Others  add  to  the  list  Regulus,  or 
a  Leonis ;  others,  a  Ursse  Majoris  and  a  Andromedas. 

THE  HISTORY  OF  THE  CONSTELLATIONS. 

THE  question  with  respect  to  the  time  when  the  stars  were 
first  grouped  into  constellations  has  been  much  discussed,  but 
cannot  be  said  to  have  been  settled.  Some  writers  believe 
that  the  earliest  division  of  the  starry  sphere  into  such  figures 
dates  back  to  fourteen  hundred  years  before  the  Christian 
era;  but  the  most  ancient  reference  to  them  in  literature  is  in 
Homer  and  Hesiod,  some  seven  hundred  and  fifty  or  eight  hun- 
dred and  fifty  years  before  Christ.  These  poets  mention  only 
a  few  of  the  more  marked  stars  and  asterisms,  as  Arcturus, 
Sirius,  the  Pleiades,  the  Hyades,  Orion,  and  the  Bear.  There 
are  references  to  certain  stars  or  groups  of  stars  in  the  Bible, 
Job  ix.  9,  xxvi.  13,  xxxviii.  31,  32;  Amos  v.  8;  but  they  are 
probably  not  more  ancient  than  those  in  the  Greek  poets,  and 
the  translation  of  the  passages  is  a  matter  of  dispute. 


APPENDIX.  333 

It  is  pretty  certain  that  nearly  four  hundred  years  before 
Christ  all  the  leading  constellations  had  been  formed  ;  for 
about  that  time  Eudoxus,  of  Cnidus,  wrote  an  account  of  them, 
which  would  appear  to  have  become  quite  a  popular  work.  It 
has  not  come  down  to  our  day,  but  we  know  that  it  was  the 
basis  of  the  famous  "  Phaenomena  '*  of  Aratus,  written  about 
270  B.  C.  This  was  the  first  attempt,  so  far  as  we  know,  to 
describe  in  verse  the  groups  and  motions  of  the  stars,  and, 
though  it  was  by  no  means  free  from  mistakes,  it  was  received 
with  the  highest  favor,  and  has  been  famous  even  down  to  our 
own  day.  It  was  translated  and  praised  by  Ovid,  by  Cicero, 
and  by  Germanicus.  Manilius  drew  from  it  in  the  preparation 
of  his  Astronomica^  and  Virgil  himself  borrowed  from  it  in  his 
Georgics. 

Ptolemy,  about  140  A.  D.,  enumerates  forty-eight  constel- 
lations, —  twenty-one  northern,  twelve  zodiacal,  and  fifteen 
southern.  We  have  described  all  the  northern,  except  Equu- 
leus,  the  Little  Horse,  which  contains  only  ten  stars,  all  below 
the  third  magnitude,  between  the  head  of  Pegasus  and  the 
Dolphin. 

The  twelve  zodiacal  constellations  are  Aries,  Taurus,  Gem- 
ini, Cancer,  Leo,  Virgo,  Libra,  Scorpio,  Sagittarius,  Capricor- 
nus,  Aquarius,  and  Pisces.  They  are  situated  along  the  line 
of  the  zodiac  (page  187),  and  have  all  been  described  above. 

Of  the  fifteen  south  of  the  zodiac,  we  have  mentioned  eight. 
The  others  are  Eridanus,  Argo  Navis,  Crater,  Centaurus,  Lu- 
pus, Ara,  and  Corona  A  us  trails. 

Eridanus,  or  the  River  Po,  winds  in  an  irregular  stream 
through  some  130°  of  the  heavens.  The  portion  of  it  which  is 
visible  in  the  latitude  of  Boston  lies  between  Orion  and  Cetus. 

Argo  Navis,  or  the  Ship  Argo,  is  one  of  the  largest  and  most 
brilliant  of  the  southern  constellations.  It  contains  two  stars 
of  the  first  magnitude,  four  of  the  second,  and  nine  of  the  third. 
Only  a  small  part  of  it,  containing  none  of  the  brightest  stars, 
rises  above  the  horizon  in  our  latitude. 

Crater,  or  the  Cup,  is  on  the  back  of  Hydra,  south  of  the 
hind  feet  of  Leo.  It  is  made  up  of  a  few  stars,  only  one  of 
which  rises  to  the  third  magnitude. 

Centaurus,  or  the  Centaur,  is  a  large  and  conspicuous  con- 


334  APPENDIX. 

stellation,  but  none  of  its  brighter  stars  are  visible  in  our  lat- 
itude. 

Ara,  or  the  Altar,  does  not  rise  above  our  horizon. 

Lttptts,  or  the  Wolf,  is  directly  south  of  Scorpio.  It  con- 
tains no  conspicuous  stars. 

Corona  Australis,  or  the  Southern  Crown,  is  a  small  group 
of  stars,  only  one  of  which  is  equal  to  the  fourth  magnitude, 
between  the  fore  legs  of  Sagittarius  and  the  Milky  Way. 

Of  the  constellations  described  by  us,  two  are  modern,  — 
Coma  Berenices,  added  by  Tycho  de  Brahe,  about  1603,  and 
Canes  Venatici,  by  Hevelius,  in  1690.  Fifty  or  sixty  more 
have  been  added  from  time  to  time,  some  of  which  have  been 
rejected  by  modern  uranographers. 

The  ancient  constellations  include  all  the  brighter  stars  in 
the  heavens,  except  in  a  small  region  about  the  south  pole. 
The  later  ones  are  mainly  made  up  of  the  small  stars  not  in- 
cluded in  these  early  asterisms,  and,  with  very  few  exceptions, 
are  not  worth  tracing. 


THE  MYTHOLOGY  OF  THE  CONSTELLATIONS. 

To  the  Greeks  the  starry  heavens  were  an  illustrated  mytho- 
logical poem.  Every  constellation  was  a  picture,  connected 
with  some  old  fable  of  gods  or  heroes.  We  shall  give  a  brief 
sketch  of  the  more  important  of  these  myths,  with  a  few  out 
of  the  many  allusions  to  them  in  ancient  and  modern  poetry. 

The  two  Bears  have  one  story.  Callisto  was  a  nymph  be- 
loved by  Jupiter,  who  changed  her  into  a  she-bear  to  save  her 
from  the  jealous  wrath  of  Juno.  But  Juno  learned  the  truth, 
and  induced  Diana  to  kill  the  bear  in  the  chase.  Jupiter  then 
placed  her  among  the  stars  as  Ursa  Major,  and  her  son  Areas 
afterwards  became  Ursa  Minor.  Juno,  indignant  at  the  honor 
thus  shown  the  objects  of  her  hatred,  persuaded  Tethys  and 
Oceanus  to  forbid  the  Bears  to  descend,  like  the  other  stars, 
into  the  sea.  Hence,  Virgil  speaks  of  the  Bears  as  "  Oceani 
metuentes  aequore  tingi";  and  Ovid,  as  "liquidique  immunia 
ponti." 

According  to  Ovid,  Juno  changed  Callisto  into  a  bear ;   and 


APPENDIX.  335 

when  Areas,  in  hunting,  was  about  to  kill  his  mother,  Jupiter 
placed  both  among  the  stars. 

Ursa  Minor  was  also  called  Phcenice,  because  the  Phoenicians 
made  it  th-eir  guide  in  navigation,  while  the  Greeks  preferred 
the  Great  Bear  for  that  purpose.  It  was  also  known  as  Cy no- 
sura  (dog's  tail}  from  its  resemblance  to  the  upturned  curl  of 
a  dog's  tail.  The  Great  Bear  was  sometimes  called  Helice 
(winding),  either  from  its  shape  or  its  curved  path.  Ovid  says, 
as  Aratus  had  said  before  him,  — 

"  Esse  cluas  Arctos  ;  quarum  Cynosura  petatur 
Sidoniis,  Helicen  Graia  carina  notet." 

Bootes  (the  Herdsman}  was  also  called  Arctophylax  and  Arc- 
furtts,  both  of  which  names  mean  the  guard  or  keeper  of  the 
bear.  According  to  some  of  the  stories,  Bootes  was  Areas ; 
according  to  others,  he  was  Icarus,  the  unfortunate  son  of 
Daedalus.  The  name  Arcturus  was  afterwards  given  to  the 
chief  star  of  the  constellation. 

Cepheus,  Cassiopeia,  Andromeda,  Perseus,  and  Pegasus  are  a 
group  of  star-pictures  illustrating  a  single  story. 

Cepheus  and  Cassiopeia  were  the  king  and  queen  of  Ethi- 
opia, and  had  a  very  beautiful  daughter,  Andromeda.  Her 
mother  boasted  that  the  maiden  was  fairer  than  the  Nereids, 
who  in  their  anger  persuaded  Neptune  to  send  a  sea-monster 
to  ravage  the  snores  of  Ethiopia.  To  appease  the  offended 
deities  Andromeda,  by  the  command  of  an  oracle,  was  exposed 
to  this  monster.  The  hero  Perseus  rescued  her  and  married 
her. 

Milton,  in  //  Penseroso,  alludes  to  Cassiopeia  as 

"  that  starred  Ethiop  queen  that  strove 
To  set  her  beauty's  praise  above 
The  Sea-Nymphs,  and  their  powers  offended." 

According  to  one  form  of  the  story,  it  was  her  own  beauty,  and 
not  her  daughter's,  of  which  the  "Ethiop  queen  "  boasted. 

Pegasus,  the  winged  horse,  sprang  from  the  blood  of  the 
frightful  Gorgon,  Medusa,  whom  Perseus  had  slain  not  long 
before  he  rescued  Andromeda  from  the  sea-monster.  Accord- 
ing to  the  most  ancient  account,  Pegasus  became  the  horse 
of  Jupiter,  for  whom  he  carried  the  thunder  and  IH 


336  APPENDIX. 

but  he  afterward  came  to  be  considered  the  horse  of  Aurora, 
and  finally  of  the  Muses.  Modern  poets  rarely  speak  of  him 
except  as  connected  with  the  Muses. 

The  Dragon,  according  to  some  of  the  poets,  was  the  one 
that  guarded  the  golden  apples  of  the  Hesperides ;  according 
to  others,  the  monster  sacred  to  Mars  which  Cadmus  killed  in 
Boeotia. 

Virgil  describes  the  dragon  thus  (G.  i.  244) :  — 

"  Maximus  hie  flexu  sinuoso  elabitur  Anguis 
Circum  perque  duas,  in  morem  fluminis,  Arctos." 

The  Lyre  is  said  to  be  the  one  which  Apollo  gave  to  Orpheus. 
After  the  death  of  Orpheus,  Jupiter  placed  it  among  the  stars 
at  the  intercession  of  Apollo  and  the  Muses. 

The  Crown  was  the  bridal  gift  of  Bacchus  to  Ariadne,  trans- 
ferred to  the  heavens  after  her  death.  Virgil  speaks  of  it  (G.  i. 
222)  as  "  Gnosia  stella  Coronae,"  referring  to  the  Cretan  birth 
of  Ariadne.  Ovid  also  calls  it  (Fasti,  iii.  457)  "Coronam  Gno- 
sida."  Spenser  refers  to  it  as  follows  :  — 

"  Look  how  the  crown  which  Ariadne  wore 
Upon  her  ivory  forehead  that  same  day 
That  Theseus  her  unto  his  bridal  bore, 
When  the  bold  Centaurs  made  that  bloody  fray 
With  the  fierce  Lapiths  which  did  them  dismay, 
Being  now  placed  in  the  firmament, 
Through  the  bright  heaven  doth  her  beams  display, 
And  is  unto  the  stars  an  ornament, 
Which  round  about  her  move  in  order  excellent." 

Hercules  is  spoken  of  by  Aratus  as  — 

"  An  Image  none  knows  certainly  to  name, 
Nor  what  he  labors  for  "  ; 

and  again,  in  another  part  of  the  poem,  as  "  the  inexplicable 
Image."  Ptolemy  refers  to  it  in  somewhat  the  same  way. 
Manilius  calls  it  "ignota  fades."  When  the  name  Hercules 
was  given  to  it  would  appear  to  be  uncertain. 

Aquila  fs  probably  the  eagle  into  which  Merops  was  changed. 
It  was  placed  among  the  stars  by  Juno.  Some,  however,  make 
it  the  Eagle  of  Jupiter.. 


APPENDIX.  337 

Cygnus  or  Cycnus,  according  to  Ovid,  was  a  relative  of 
Phaethon.  While  lamenting  the  unhappy  fate  of  his  kinsman 
on  the  banks  of  the  Eridanus,  he  was  changed  by  Apollo  into  a 
swan,  and  placed  among  the  stars. 

Sagittarius  was  said  by  the  Greeks  to  be  the  Centaur 
Cheiron,  the  instructor  of  Peleus,  Achilles,  and  Diomed.  It 
is  pretty  certain,  however,  that  all  the  zodiacal  constellations 
are  of  Egyptian  origin,  and  represent  twelve  Egyptian  dei- 
ties who  presided  over  the  months  of  the  year.  Thus  Aries 
was  Jupiter  Ammon  ;  Taurus,  the  bull  Apis  ;  Gemini,  the  in- 
separable gods  Horus  and  Harpocrates  ;  and  so  on.  The 
Greeks  adopted  the  figures,  and  invented  stones  of  their  own 
to  explain  them. 

Scorpio,  in  the  Egyptian  zodiac,  represented  the  monster 
Typhon.  Originally  this  constellation  extended  also  over  the 
space  now  filled  by  Libra.  Thus  Ovid  (Met.  ii.  195)  says  :  — 

"  Est  locus,  in  geminos  ubi  brachia  concavat  arcus 
Scorpios,  et  cauda  flexisque  utrimque  lacertis 
Porrigit  in  spatium  signorum  membra  duorum" 

Virgil  also  (G.  i.  33)  suggests  that  the  deified  Augustus  may 
find  a  place  among  the  stars,  — 

"  Qua  locus  Erigonen  inter  Chelasque  sequentes 

Panclitur." 

Erigone  is  Virgo,  and  Chela  are  the  claws  of  the  Scorpion. 
The  poet  goes  on  to  picture  the  Scorpion  as  drawing  himself 
into  narrower  space,  to  make  room  for  the  new-comer:  — 

"  Ipse  tibi  jam  brachia  contrahit  ardens 
Scorpios,  et  caeli  justa  plus  parte  reliquit." 

Ophiuchus  represents  /Esculapius,  the  god  pf  medicine.  Ser- 
pents were  sacred  to  him,  "  probably  because  they  were  a  sym- 
bol of  prudence  and  renovation,  and  were  believed  to  have  the 
power  of  discovering  herbs  of  wondrous  powers." 

Milton  (P.  L.  ii.  709)  speaks  of 

"  the  length  of  Ophiuchus  huge 
In  the  arctic  sky." 

Aquarius,  in   Greek  fable,   was   Ganymede,   the   Phrygian 
boy  who  became  the  cup-bearer  of  the  gods  in  place  of  Hebe. 
15  v 


338  APPENDIX. 

Capricornus,  the  god  Mendes  in  the  Egyptian  zodiac,  is  the 
subject  of  several  Greek  fables  not  worth  recounting. 

There  are  various  stories  also  with  regard  to  Auriga.  The 
star  Capella  takes  its  name  from  the  goat  which  he  bears  on 
his  shoulder.  Aratus  says  (Dr.  Frothingham's  translation):  — 

"  On  his  left  shoulder  rests 
The  sacred  Goat,  — said  to  have  suckled  Jove  ; 
Olenian  Goat  of  Jove  the  priests  have  named  her." 

So  Ovid  (Fasti  v.  112):  — 

"  Nascitur  Oleniae  signum  pluviale  Capellae." 

Taurus,  as  has  been  staled  above,  was  the  Egyptian  Apis. 
The  Greeks  made  it  the  bull  which  carried  off  Europa.  The 
Pleiades  are  usually  called  the  daughters  of  Atlas,  whence  their 
name  Atlantides.  Milton  (P.  L.  x.  673)  speaks  of  them  as  "  the 
seven  Atlantic  Sisters."  The  idea  that  only  six  of  the  seven 
can  be  seen  is  very  ancient.  Aratus  says  :  — 

"  As  seven  their  fame  is  on  the  tongues  of  men, 
Though  six  alone  are  beaming  on  the  eye." 

And  Ovid  (Fasti  iv.  167) :  — 

"  Quae  septem  diet,  sex  tamen  esse  solent." 

According  to  one  legend  the  seventh  was  Sterope,  who  be- 
came invisible  because  she  had  loved  a  mortal ;  according  to 
another,  her  name  was  Electra,  and  she  left  her  place  that  she 
might  not  witness  the  downfall  o/  Troy,  which  was  founded  by 
her  son,  Dardanus.  Tennyson,  in  Locksley  Hall,  alludes  to  the 
Pleiades :  — 

"  Many  a  night  I  saw  the  Pleiads,  rising  through  the  mellow  shade, 
Glitter  like  a  swarm  of  fire-flies  tangled  in  a  silver  braid." 

The  H jades,  according  to  one  of  several  stories,  were  sisters 
of  the  Pleiades.  The  name  probably  means  the  Rainy,  since 
their  heliacal  rising  announced  wet  weather.  Hence  Virgil 
speaks  of  them  -as  pluviae,  and  Horace  as  tristes. 

Cetus  is  said  by  most  writers  to  be  the  sea-monster  from 
which  Perseus  rescued  Andromeda. 

Orion  was  a  famous  giant  and  hunter,  who  loved  the  daughter 
of  CEnopion,  King  of  Chios.  As  her  father  was  slow  to  con- 


APPENDIX.  339 

sent  to  her  marriage,  Orion  attempted  to  carry  off  the  maiden  ; 
whereupon  (Enopion,  with  the  help  of  Bacchus,  put  out  his 
eyes.  But  the  hero,  in  obedience  to  an  oracle,  exposed  his 
eye-balls  to  the  rays  of  the  rising  sun,  and  thus  regained  his 
sight.  The  accounts  of  his  subsequent  life,  and  of  his  death, 
are  various  and  conflicting.  According  to  some,  Aurora  loved 
him  and  carried  him  off;  but,  as  the  gods  were  angry  at  this, 
Diana  killed  him  with  an  arrow.  Others  say  that  Diana  loved 
him,  and  that  Apollo,  indignant  at  his  sister's  affection  for  the 
hero,  once  pointed  out  a  distant  object  on  the  surface  of  the 
sea,  and  challenged  her  to  hit  it.  It  was  the  head  of  Orion 
swimming,  and  the  unerring  shot  of  the  goddess  pierced  it  with 
a  fatal  wound.  Another  fable  asserts  that  Orion  boasted  that 
he  would  conquer  every  animal;  but  the  earth  sent  forth  a 
scorpion  which  destroyed  him. 
Aratus  alludes  to  the  brilliancy  of  this  constellation :  — 

"  What  eye  can  pass  him  over, 
Spreading  aloft  in  the  clear  night  ?    Him  first 
Whoever  scans  the  heavens  is  sure  to  trace." 

And  again  he  speaks  of  him  as 

"  In  nothing  mean,  glittering  in  belt  and  shoulders, 
And  trusting  in  the  might  of  his  good  sword." 

Ovid  calls  him  "  ensiger  Orion,"  and  Virgil  describes  him  as 
"armatum  auro."  We  have  a  vivid  picture  of  him  in  Long- 
fellow's "  Occultation  of  Orion  "  :  — 

"  Begirt  with  many  a  blazing  star, 
Stood  the  great  giant  Algebar, 
Orion,  hunter  of  the  beast ! 
His  sword  hung  gleaming  by  his  side, 
And,  on  his  arm,  the  lion's  hide 
Scattered  across  the  midnight  air 
The  golden  radiance  of  its  hair." 

Cants  Major  and  Minor  are  the  dogs  of  Orion,  and  are  pur- 
suing the  Hare. 

The  Twins,  Castor  and  Pollux,  the  sons  of  Jupiter  and  Leda, 
are  the  theme  of  many  a  fable.  They  were  especially  worshipped 
as  the  protectors  of  those  who  sailed  the  seas,  for  Neptune  had 


34°  APPENDIX. 

rewarded  their  brotherly  love  by  giving  them  power  over  winds 
and  waves,  that  they  might  assist  the  shipwrecked. 

Leo,  according  to  the  Greek  story,  was  the  famous  Nemean 
lion  slain  by  Hercules.  Jupiter  placed  it  in  the  heavens  in 
honor  of  the  exploit. 

The  Hydra  also  commemorates  one  of  the  twelve  labors  of 
Hercules,  —  the  destruction  of  the  hundred-headed  monster  of 
the  Lernsean  lake. 

Virgo  represents  Astraea,  the  goddess  of  innocence  and 
purity,  or,  as  some  say,  of  justice.  She  was  the  last  of  the 
gods  to  withdraw  from  earth  at  the  close  of  "  the  golden  age." 
Aratus  thus  speaks  of  her :  — 

"  Once  on  earth 

She  made  abode,  and  deigned  to  dwell  with  mortals. 
In  those  old  times,  never  of  men  or  dames 
She  shunned  the  converse  ;  but  sat  with  the  rest, 
Immortal  as  she  was.     They  called  her  Justice. 
Gathering  the  elders  in  the  public  forum, 
Or  in  the  open  highway,  earnestly 
She  chanted  forth  laws  for  the  general  weal." 

But  when  the  age  became  degenerate, 

"  Justice  then,  hating  that  generation, 
Flew  heavenward,  and  inhabited  that  spot 
Where  now  at  night  may  still  be  seen  the  Virgin." 

Libra,  or  the  Balance,  is  the  emblem  of  justice,  and  is  usually 
associated  with  the  fable  of  Astraea. 

Argo  Navis  is  the  famous  ship  in  which  Jason  and  his  com- 
panions sailed  to  find  the  Golden  Fleece. 

This  slight  sketch  of  the  leading  fables  connected  with  the 
constellations  will  serve  to  show  how  completely  the  Greeks 
"nationalized  the  heavens."  There  have  been  various  at- 
tempts to  change  into  Christian  titles  the  whole  nomenclature 
of  the  skies.  Julius  Schiller,  in  1627,  urged  such  a  revolution 
in  his  Coelum  Stellatum  Christianum,  as  Bartsch  and  others 
had  done  before  him.  According  to  these  reformers  of  the 
heavens,  the  Great  Bear  becomes  the  skiff  of  St.  Peter ;  Cas- 
siopeia, Mary  Magdalene;  and  Perseus  with  Medusa's  head, 
David  with  the  head  of  Goliath.  The  cross  in  the  Swan  is  the 


APPENDIX.  341 

Holy  Cross ;  the  Virgin  is  Mary ;  and  the  Water-bearer,  John 
the  Baptist. 

In  the  seventeenth  century  Weigel,  a  professor  in  the  Uni- 
versity of  Jena,  proposed  the  formation  of  a  collection  of  he- 
raldic constellations.  In  the  zodiac  he  wished  to  place  the 
escutcheons  of  the  twelve  most  illustrious  houses  of  Europe ; 
and  Orion,  Auriga,  and  other  leading  asterisms  were  metamor- 
phosed in  the  same  way. 

Sir  John  Herschel  says :  "  The  constellations  seem  to  have 
been  almost  purposely  named  and  delineated  to  cause  as  much 
confusion  and  inconvenience  as  possible.  Innumerable  snakes 
twine  through  long  and  contorted  areas  of  the  heavens,  where 
no  memory  can  follow  them.  Bears,  lions,  and  fishes,  small 
and  large,  northern  and  southern,  confuse  all  nomenclature. 
A  better  system  of  constellations  might  have  been  a  material 
help  as  an  artificial  memory." 

But  the  habits  of  four  thousand  years  are  not  easily  changed. 
Men  will  still 

"  Hold  to  the  fair  illusions  of  old  time,  — 
Illusions  that  shed  brightness  over  life, 
And  glory  over  nature  "  ; 

and  the  starry  heavens  will  continue  to  be  for  ages  to  come, 
as  they  have  been  for  ages  gone  by,  a  picture-book  of  Greek 
fable. 


QUESTIONS    FOR   REVIEW   AND 
EXAMINATION. 


MOTIONS  AND  DISTANCES   OF  THE   HEAVENLY 
BODIES. 

I.  WHAT  was  the  earth  once  thought  to  be  ?  2.  What  is 
the  shape  of  the  earth  now  known  to  be  ?  3.  How  is  this 
shown  by  observation  of  ships  at  sea?  4.  How  by  the  ob- 
servation of  the  eclipses  of  the  moon  ?  5.  How  do  we  know 
that  the  sun,  moon,  and  planets  are  all  globes  ?  6.  What  is 
known  of  the  shape  of  the  stars  ?  7.  How  do  the  stars  rise 
and  set  ?  8.  What  are  circumpolar  stars  ?  9.  What  is  true 
of  the  motion  of  the  Polar  Star  ?  10.  What  is  true  of  the 
motion  of  the  stars  as  we  go  from  the  Polar  Star?  n.  How 
do  we  know  that  the  stars  describe  accurate  circles  about  the 
Polar  Star  as  a  centre  ?  12.  How  do  we  know  that  the  stars 
move  at  a  uniform  rate,  and  all  describe  their  circles  in  the 
same  time  ?  13.  How  do  we  detect  the  existence  of  atmos- 
pheric refraction  ?  14.  What  is  the  effect  of  refraction  upon 
all  the  heavenly  bodies  ?  15.  Explain  this  effect  ?  16. 
Prove  that  the  earth  rotates  from  west  to  east  in  24  hours  ? 
17.  Do  the  heavens  really  rotate  about  the  earth  from  east 
to  west?  18.  How  do  we  know  this?  19.  State  the  direc- 
tion of  the  circles  described  by  the  stars,  as  compared  with 
that  of  the  horizon  in  different  parts  of  .the  earth  ?  20.  Do 
the  stars  as  seen  in  different  parts  of  the  earth  describe  cir- 
cles which  really  have  different  directions  ?  21.  Show  by  an 
illustration  that  two  co-ordinates  are  sufficient  to  define  the 
position  of  a  point  on  a  plane  surface  ?  22.  What  two  co-or- 
dinates serve  to  define  the  position  of  a  point  on  the  sur- 
face of  a  globe  ?  23.  Show  that  these  co-ordinates  will  serve 
to  define  the  position  of  such  a  point  ?  24.  What  are  the 
most  convenient  co-ordinates  of  a  star  ?  25.  Which  of  these 


344         QUESTIONS    FOR    REVIEW   AND    EXAMINATION. 

co-ordinates  is  measured  by  means  of  the  transit  instrument  ? 
26.  Explain  the  adjustment  of  this  instrument.  27.  Explain 
how  one  of  the  co-ordinates  of  a  star  is  measured  with  it. 
28.  What  is  a  sidereal  day?  29.  Describe  the  mural  circle. 

30.  Explain  how  the  horizontal  reading  of  the  circle  is  found. 

31.  Explain    how  the  altitude   of  the  celestial  pole  is   found. 

32.  Which   co-ordinate  of  a   heavenly  body  is  found   by  the 
mural  circle  ?     33.  Explain  how.     34.  Do  the  fixed  stars  ap- 
pear in  exactly  the  same  position  in  the  heavens,  from  what- 
ever part  of  the  earth  they  are  observed  ?     35.  How  do  we 
know  ?     36.  What  is  the   solar  day  ?     37.  How  is  its  length 
found,  and  h6w  does  it  compare  with  that  of  the  sidereal  clay  ? 
38.  What  does   the   difference   of  length  of  these   two   days 
show  as  to  one  of  the  co-ordinates  of  the  sun  ?     39.  By  what 
other  observation  is  this  same  thing  shown  ?    40.  What  is  a 
sidereal  year?     41.  How  do  the  solar  days  compare  with  one 
another  in  length  ?     42.  Why  is  ordinary  clock  time   called 
mean  time  ?     43.  What  is  the  ecliptic  ?    44.  What  is  the  in- 
clination of  the  ecliptic  to  the  earth's  axis  ?    45.  What  belt 
of  the  earth  is  called  the  torrid  zone  ?     46.  What  belts  are 
called  the  frigid  zones  ?    47.  What  belts  are  called  the  temper- 
ate zones  ?     48.  What  is  true  of  the  sun's  coming  directly 
overhead,  and  of  its  rising  and  setting  in  each  of  these  zones  ? 
49.  Explain   the   changes  in  the   relative  lengths  of  day  and 
night.    50.  Explain  the  change  of  seasons.    51.  What  is  the  ce- 
lestial equator  ?     52.  Explain  declination  and  right  ascension. 
53.  What  are  the  equinoxes  ?     54.  What  is  the  precession  of 
the  equinoxes  ?     55.  What  is  the  tropical  year?     56.  How  does 
it  compare   with  the   sidereal  year  ?     57.  Which  is   the  year 
of  common  life  ?     58.  What  are  the  solstices  ?    59.  What  does 
the  variation  of  the  sun's  apparent  diameter  prove  ?     60.  How 
can  the  form  of  the  path  descried  by  the  sun  among  the  stars 
be   found?     61.  What  kind   of  a  curve   is  it?     62.  To  what 
does   the  inclination  of  the  earth's  axis  to   the   ecliptic   give 
rise?     63.  What  is  twilight?     64.  What  causes   it?     65.  It 
continues  while  the  sun  is  within  what  distance  of  the  hori- 
zon ?     66.  When  and  where  is  twilight  shortest  ?     67.  Explain 
why  this  is  so.     68.  In  the  latitude  of  Boston   how  does  the 
twilight   in   the   summer  compare   with   that   in   the    winter  ? 


QUESTIONS    FOR   REVIEW   AND    EXAMINATION.          345 

69.  Explain  why  it  is  so.  70.  Where  is  the  new  moon  always 
seen  ?  71.  What  is  her  motion?  72.  When  is  the  moon  in 
conjunction  ?  73.  When  in  opposition  ?  74.  What  is  true  of 
the  moon's  declination  ?  75.  What  are  the  moon's  nodes  ? 
76.  What  is  a  lunar  day,  and  how  does  it  compare  with  the 
solar  day  ?  77.  How  do  lunar  days  compare  with  one  another  ? 
78.  What  is  the  moon's  orbit,  and  how  can  it  be  found  ?  79. 
What  is  meant  by  the  moon's  being  in  perigee  ?  80.  What  by 
her  being  in  apogee?  81.  What  is  the  line  of  apsides  ?  82. 
Describe  the  apparent  motion  of  Venus.  83.  The  apparent 
motion  of  Mercury.  84.  Why  are  these  bodies  called  plan- 
ets ?  85.  What  is  meant  by  the  greatest  elongation  of  these 
planets  ?  86.  Describe  the  apparent  motion  of  the  other  plan- 
ets. 87.  How  did  the  ancients  attempt  to  explain  the  ap- 
parent irregular  motion  of  the  planets  ?  88.  Give  an  account 
of  the  Ptolemaic  system.  89.  Explain  what  is  meant  by 
cycles,  epicycles,  and  deferents.  90.  What  change  did  Tycho 
de  Brahe  introduce  into  this  system?  91.  How  was  this  sys- 
tem further  modified  by  Copernicus  ?  92.  Did  he  dispense  with 
epicycles  and  deferents  in  his  system.?  93.  What  three  facts 
did  Kepler  discover  about  the  planetary  motions  ?  94.  Give 
an  account  of  the  method  by  which  he  discovered  these  facts. 
95.  Whose  observations  did  he  make  use  of?  96.  What  is  the 
sidereal  period  of  a  planet  ?  97.  What  is  the  synodical  period 
of  a  planet  ?  98.  How  is  the  sidereal  period  of  the  earth 
found  ?  99.  How  is  the  synodical  period  of  a  planet  found  ? 
100.  What  planets  can  be  in  inferior  and  superior  conjunc- 
tion ?  101.  What  planets  have  conjunctions  and  oppositions? 
102.  What  must  be  known  in  order  to  compute  the  sidereal 
period  of  a  planet  ?  103.  Find  the  sidereal  period  of  an 
inferior  planet.  104.  Find  the  sidereal  period  of  a  superior 
planet.  105.  What  must  be  observed  in  order  to  find  the  rel- 
ative distance  of  an  inferior  planet  from  the  sun  ?  106.  Find 
the  relative  distance  of  an  inferior  planet  from  the  sun. 
107.  What  must  be  observed  in  order  to  find  the  relative  dis- 
tance of  a  superior  planet  from  the  sun  ?  108.  Find  the  rela- 
tive distance  of  a  superior  planet  from  the  sun.  109.  When 
the  relative  distances  of  the  planets  from  the  sun  are  known, 
what  must  be  found  in  order  to  ascertain  their  real  distances 


346          QUESTIONS    FOR    REVIEW   AND    EXAMINATION, 

from  the  sun?  no.  By  means  of  what  is  the  distance  from 
the  earth  to  the  sun  found?  in.  Find  the  distance  in  miles 
between  the  chords  which  two  observers  see  Venus  describe 
across  the  sun's  disc,  supposing  that  we  know  the  distance  be- 
tween the  observers  in  miles.  112.  What  observation  is  ne- 
cessary to  find  the  length  of  the  two  chords  in  degrees  and 
minutes?  113.  Explain  how  we  find  the  length  of  these 
chords  in  degrees  and  minutes,  and  of  the  radius  of  the  sun. 
114.  Find  the  distance  between  these  two  chords  in  angular 
measurement.  115.  Find  the  angle  which  the  radius  of  the 
earth  would  subtend  at  the  distance  of  the  sun.  116.  Know- 
ing this  angle,  find  the  distance  of  the  earth  from  the  sun. 
117.  Explain  how  the  length  of  the  earth's  radius  can  be 
found.  1 1 8.  Explain  how  we  find  what  fraction  of  a  whole 
meridian  the  arc  included  between  two  places  is.  119.  Ex- 
plain how  we  can  find  the  distance  between  two  points  by 
triangulation.  120.  Give  an  account  of  the  measurement  of 
a  base  line.  121.  Why  is  so  great  care  necessary  in  the  meas- 
urement of  the  base  line?  122.  Explain  how  a  system  of  tri- 
angles can  be  constructed  between  two  points,  and  how  their 
parts  can  be  computed.  123,  Explain  how  the  distance  be- 
tween the  two  points  can  be  found  after  the  system  of  triangles 
has  been  constructed.  124.  How  do  we  know  that  the  earth 
is  not  an  exact  sphere  ?  125.  Is  the  exact  distance  from  the 
earth  to  the  sun  known  ?  126.  How  can  the  real  distance  of 
the  planets  from  the  sun  be  found,  after  their  relative  distance 
and  the  distance  of  the  earth  is  known  ?  127.  How  did  the 
ancients  find  the  distance  of  the  moon  from  the  earth  approx- 
imately ?  128.  What  is  parallax?  129.  Show  that  we  real- 
ly judge  of  the  distances  of  ordinary  objects  by  means  of  par- 
allax. 130.  In  finding  the  parallax  of  the  moon  what  takes 
the  place  of  the  two  eyes?  131.  Explain  how  the  difference 
of  direction  of  two  telescopes,  when  pointed  at  the  moon  from 
different  parts  of  the  earth,  can  be  found  by  measuring  the 
moon's  polar  distance  at  each  place.  132.  Explain  how  the 
moon's  parallax  is  found  when  the  difference  of  direction  of 
the  telescopes  is  known.  133.  Explain  how  this  difference  of 
direction  can  be  found  by  measuring  at  each  place  the  distance 
of  the  moon  from  a  star  near  which  she  passes.  134.  Why 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.         347 

is  the  latter  method  preferable  to  the  former?  135.  Give  a 
general  account  of  the  orbits  of  the  planets.  136.  What  are 
nodes  ?  137.  Explain  why  the  transits  of  Venus  occur  so  sel- 
dom. 138.  Explain  how  we  estimate  the  distance  of  an  ob- 
ject by  using  only  one  eye.  139.  What  is  found  to  be  true 
when  a  telescope  is  pointed  to  certain  fixed  stars  at  inter- 
vals of  six  months  ?  140.  What  is  one  way  of  finding  whether 
the  direction  of  the  telescope  would  be  the  same  at  both  ob- 
servatories ?  141.  Explain  precession.  142.  What  is  nuta- 
tion ?  143.  What  is  aberration  of  light  ?  144.  What  is  its 
effect  upon  the  position  of  a  star?  145-  Explain  the  second 
method  of  finding  the  parallax  of  a  star.  146.  What  is  true 
of  the  distance  of  the  stars  ?  147.  Name  some  of  the  re- 
markable nebulae.  148.  What  has  led  astronomers  to  be- 
lieve that  many  of  the  nebulae  are  systems  of  stars  ?  149. 
How  did  Herschel  believe  our  sidereal  system  would  ap- 
pear at  the  distance  of  the  nebulae?  150.  What  is  true  of 
the  motion  of  the  planets  and  satellites  of  our  solar  system  ? 
151.  Are  the  stars  really  fixed?  152.  Show  that  our  sun  is 
moving  through  space.  153.  Give  an  example  of  a  double 
star.  154.  What  is  the  difference  between  a  physically  and 
an  optically  double  star  ?  155.  Give  an  account  of  Theta  Ori- 
onis.  156.  Of  Xi  Ursae  Majoris.  157.  What  is  true  of  the 
length  of  the  periods  of  the  binary  stars  ?  158.  What,  of  the 
dimensions  of  their  orbits  ?  159.  Are  the  physically  connect- 
ed systems  of  stars  numerous  ?  160.  Show  that  the  sun  is 
a  star.  161.  What  seems  to  be  true  of  all  the  heavenly 
bodies?  162.  How  do  the  velocities  with  which  the  stars 
are  moving  compare  with  the  earth's  velocity  in  its  orbit? 

PHYSICAL  FEATURES  OF  THE  HEAVENLY  BODIES. 

163.  Explain   how  we  may  find  the  diameter  of  the  sun. 

164.  How   does    the   sun   compare   with    the   earth    in    size  ? 

165.  What  are  sun-spots  ?     166.  At  what  intervals  are  they 
most  frequent  ?     167.  Give  an  account  of  the  movements  of 
these   spots.      168.  Show  that  these  spots  are  not  planets. 

169.  Show  that  the  sun  rotates  on  his  axis  in  about  25  days. 

170.  Show  that  the   sun's  axis  is   not  perpendicular  to  the 


348         QUESTIONS    FOR   REVIEW   AND    EXAMINATION. 

ecliptic.  171.  Describe  the  appearances  of  the  spots.  172.  What 
are  tne  dimensions  of  the  sun-spots  ?  173.  Give  an  account  of 
the  changes  which  they  undergo.-  174.  Give  an  account  of  the 
faculae.  175.  Give  an  account  of  the  "pores"  and  "willow 
leaves."  176.  Give  an  account  of  the  corona.  177.  Of  the 
rose-colored  clouds.  178.  What  were  Wilson's  observations 
and  conclusions  with  reference  to  the  sun-spots  ?  179.  What  is 
Herschel's  theory  of  the  sun-spots  ?  180.  Give  some  account 
of  the  investigations  of  De  La  Rue,  Stewart,  and  Loewy. 
181.  How  have  they  shown  that  the  faculae  are  elevations  of  the 
sun's  photosphere  ?  182.  What  do  they  consider  to  be  the  na- 
ture of  the  photosphere  ?  183.  What  have  they  found  to  be  the 
usual  position  of  the  faculae?  184.  How  do  they  think  the 
spots  and  faculae  are  formed  ?  185.  How  have  they  shown  that 
Venus  and  Jupiter  have  an  influence  on  the  formation  of  the 
spots?  1 86.  Why  is  Mercury  seldom  seen  as  a  conspicuous 
object?  187.  What  is  the  shape  of  his  orbit?  188.  What  is 
its  inclination  to  the  ecliptic?  189.  How  do  we  know  that 
Mercury  is  an  exact  sphere  ?  190.  How  does  the  diameter  of 
Mercury  compare  with  that  of  the  earth?  191.  Explain  the 
phases  of  Mercury.  192.  Is  there  any  evidence  of  the  existence 
of  mountains  on  the  planet  ?  193.  What  led  Schroter  to  think 
that  Mercury  rotates  on  his  axis  in  about  24  hours  ?  194.  What 
did  Schroter  think  to  be  the  inclination  of  Mercury's  axis  to 
the  plane  of  his  orbit  ?  195.  What  led  him  to  this  conclusion  ? 
196.  Give  an  account  of  Mercury's  seasons  on  the  supposition 
that  this  inclination  is  correct.  197.  Show  that  this  planet  has 
an  atmosphere.  198.  What  is  the  second  planet  from  the  sun. 
199.  What  is  the  form  of  her  orbit  ?  200.  How  does  her  di- 
ameter compare  with  that  of  the  earth  ?  201.  By  what  names 
is  Venus  familiarly  known  ?  202.  Explain  her  phases.  203.  In 
what  position  is  Venus  most  brilliant  ?  204.  What  indicates 
that  there  are  mountains  on  Venus  ?  205.  According  to  Schro- 
ter what  is  the  period  of  her  axial  rotation  ?  206.  Has  Venus 
an  atmosphere  ?  207.  Has  she  a  moon  ?  208.  Give  an  ac- 
count of  the  Zodiacal  Light  209.  What  have  been  the  suppo- 
sitions with  reference  to  the  nature  of  this  light?  210.  What  is 
the  third  planet  from  the  sun  ?  211.  What  is  the  inclination  of 
its  axis  to  the  ecliptic?  212.  What  is  its  diameter?  213.  By 


QUESTIONS   FOR   REVIEW  AND    EXAMINATION.          349 

what  is  the  earth  attended  ?  214.  What  is  the  interval  between 
two  successive  new  moons  ?  215.  Give  an  account  of  the  phases 
of  the  moon.  216.  Explain  the  moon's  libration  in  longitude. 
217.  Explain  her  libration  in  latitude.  218.  Explain  her  paral- 
lactic  libration.  219.  Give  an  account  of  the  earth's  phases  as 
seen  from  the  moon.  220.  When  does  the  moon  appear 
largest?  221.  Show  that  the  moon  is  nearer  when  in  the 
zenith  than  when  at  the  horizon.  222.  What  is  true  of  the  ap- 
parent size  of  the  moon  as  compared  with  her  real  size  ? 
223.  What  kind  of  a  path  does  the  moon  describe  through 
space?  224.  Give  an  account  of  the  harvest  moon.  225.  Give 
an  account  of  the  surface  of  the  moon.  226.  Show  how  the 
height  of  a  lunar  mountain  can  be  found.  227.  Give  an  account 
of  Tycho.  228.  Of  Copernicus.  229.  Of  Kepler.  230.  Of 
Eratosthenes.  231.  Are  there  active  volcanoes  on  the  moon? 
232.  Give  an  account  of  the  crater  Linne*.  233.  Show  that  the 
moon  has  no  atmosphere.  234.  What  have  some  thought  to 
exist  on  the  side  of  the  moon  turned  from  us  ?  235.  What  is 
the  form  of  the  shadows  of  the  earth  and  moon  ?  236.  What 
is  the  umbra,  and  what  the  penumbra,  of  these  shadows  ? 
237.  Explain  when  an  eclipse  may  occur.  238.  Explain  each 
of  the  three  kinds  of  eclipses  of  the  sun  ?  239.  What  are  the 
conditions  under  which  a  total  eclipse  of  the  sun  is  possible  ? 
240.  Do  total  eclipses  of  the  sun  often  occur  ?  241.  Give 
Hind's  account  of  the  total  eclipse  of  1851.  242.  How  many 
kinds  of  eclipses  of  the  moon  may  there  be  ?  243.  What 
is  the  fundamental  difference  between  eclipses  of  the  sun 
and  of  the  moon  ?  244.  When  is  a  lunar  eclipse  central  ? 

245.  Upon  what  does  the  magnitude  of  a  lunar  eclipse  depend? 

246.  Does  the  moon  become  invisible  during  a  total  eclipse  ? 

247.  After  what  intervals  do  the  eclipses  of.  the  sun  and  moon 
repeat  themselves  ?     248.  What  is  an  occultation  ?     249.  Ex- 
plain how  longitude  at  sea  is  ascertained  by  the  motion  of  the 
moon    among    the    stars.      250.    What    are   shooting    stars? 
251.    At  what  season  of  the    year    are    shooting    stars    most 
numerous  ?      252.   At  what  intervals  is  the  November  shower 
particularly  brilliant?     253.  Give  an  account  of  the  shower  of 
1799.     254.  What  has  led  astronomers  to  attribute  the  August 
and  November  showers  to  the  passage  of  the  earth  through 


350         QUESTIONS    FOR    REVIEW   AND    EXAMINATION. 

meteoric  rings  at  these  times  ?  255.  Do  these  meteoric  bodies 
ever  fall  to  the  earth  ?  256.  Why  is  Mars  called  an  exterior  or 
superior  planet  ?  257.  How  does  the  size  of  Mars  compare 
with  that  of  the  earth  ?  258.  When  is  Mars  situated  most 
favorably  for  observation  ?  259.  What  are  the  physical  char- 
acteristics of  Mars  ?  260.  Why  does  Mars  experience  about 
the  same  change  of  seasons  as  the  earth?  261.  How  do  we 
know  that  Mars  has  an  atmosphere  of  considerable  density  ? 
262.  Which  planets  belong  to  the  inner  group,  and  what  are 
ttheir  resemblances  ?  263.  What  led  Kepler  to  suspect  that  a 
planet  existed  between  Mars  and  Jupiter  ?  264.  What  led  to  a 
systematic  search  for  the  suspected  planet  ?  265.  What  is 
Bode's  law  of  planetary  distances  ?  266.  Give  an  account  of 
the  discovery  of  Ceres.  267.  Of  the  discovery  of  Pallas. 
268.  What  led  Dr.  Olbers  to  think  that  Ceres  and  Pallas  were 
fragments  of  a  broken  planet  ?  269.  When  and  by  whom  was 
Juno  discovered  ?  270.  Give  an  account  of  the  discovery  of 
Vesta.  271.  Give  an  account  of  the  discovery  of  Astrasa. 
272.  What  is  this  group  of  planets  called  ?  273.  How  many 
are  now  known  to  exist  ?  274.  How  do  their  orbits  differ  from 
those  of  the  larger  planets  ?  275.  What  is  the  first  planet 
outside  of  this  group  ?  276.  What  is  true  of  his  brightness  ? 

277.  How  does    his   size   compare   with    that  of   the   earth  ? 

278.  Is  Jupiter  a   perfect   sphere  ?     279.    Describe  Jupiter's 
belts.     280.  In  what  time  does  Jupiter  perform  his  axial  rota- 
tion ?      281.    How  was    this   ascertained?      282.    How   many 
moons  has  Jupiter  ?     283.  When  and  by  whom  were  they  dis- 
covered ?     284.  What  is  true  of  their  configurations  and  their 
axial  rotations  ?     285.  Give   an   account  of   the   occupations, 
eclipses,  and  transits  of  Jupiter's  moons.     286.  What  is  the 
planet  next  outside  of  Jupiter  ?     287.  How  does  the  bulk  of 
Saturn  compare  with  that  of  Jupiter  ?     288.  How  many  moons 
has  Saturn  ?     289.  Give  an  account  of  the  discovery  of  Saturn's 
rings.      290.  Explain  the  various  appearances  of  these  rings. 
291.  What  is  true  of  their  number?     292.  What  are  some  of 
the  conjectures  PS  to  their  nature?     293.    Previous  to  1781, 
what  planets  were  known  ?     294.  What  planet  was  discovered 
in  that  year?   295.  Give  an  account  of  its  discovery.   296.  How 
does   the   size   of  Uranus  compare  with   that  of  the  earth  ? 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.          351 

297.  Why  do  we  not  know  the  period  of  its  rotation  ?  298.  How 
many  moons  has  it  ?  299.  What  is  there  peculiar  about  their 
motion  ?  300.  What  is  the  most  distant  planet  now  known  to 
exist?  301.  Is  its  period  of  rotation  known?  302.  What  is 
peculiar  about  its  moon  ?  303.  Give  an  account  of  the  dis- 
covery of  Neptune  ?  304.  Which  planets  belong  to  the  outer 
group,  and  in  what  do  they  resemble  one  another  ?  305.  What 
is  common  to  the  motions  of  all  the  planets  and  moons  ? 
306.  Give  a  general  description  of  the  comets.  307.  Give  an 
account  of  some  of  the  most  famous  comets.  308.  To  what 
is  the  twinkling  of  the  stars  due  ?  309.  What  is  the  whole 
number  of  stars  visible  to  the  naked  eye?  310.  How  many 
stars  are  there  of  the  first  magnitude  ?  311.  How  many  of  the 
second  magnitude  ?  312.  How  many  of  the  third  ?  313.  What 
is  the  number  of  the  telescopic  stars  ?  314.  What  are  the  con- 
stellations ?  315.  Name  the  zodiacal  constellations.  316.  Ex- 
plain the  naming  of  the  stars.  317.  What  is  true  of  the  color 
of  the  stars?  318.  What  are  variable  stars?  319.  Give  an 
account  of  Algol  and  Mira.  320.  What  are  irregular  or  tem- 
porary stars?  321.  Give  an  account  of  some  of  the  most 
famous  of  these  stars-  322.  Give  an  account  of  the  Milky  Way. 
323.  What  did  Herschel  believe  to  be  the  form  of  our  side- 
real system  ?  324.  Mention  some  clusters  of  stars  that  are 
visible  to  the  unaided  eye.  325.  Give  an  account  of  the  tele- 
scopic cluster  in  Hercules,  and  that  in  Centaurus.  326.  What 
are  nebulous  stars  ?  327.  Are  the  nebulae  ever  variable  ? 
328.  Give  an  account  of  the  Magellanic  clouds.  329.  By  what 
other  name  are  they  known  ? 


GRAVITY. 

330.  What  is  the  first  law  of  motion  ?  331.  How  is  this 
law  established  ?  332.  Show  that  the  planets  and  their  moons 
are  acted  upon  by  some  force.  333.  What  is  the  second  law 
of  motion  ?  334.  How  is  this  law  established  ?  335.  De- 
scribe Atwood's  machine.  336.  Show  upon  what  the  form  of 
the  curve  described  by  a  moving  body  depends.  337.  Show 
that  the  force  which  curves  the  path  of  the  planets  is  always 
directed  towards  the  sun.  338.  Show  that  gravity  would 


352          QUESTIONS    FOR    REVIEW  AND    EXAMINATION. 

cause  all  bodies  to  fall  at  the  same  rate,  were  it  not  for  the 
air.  339.  Describe  the  pendulum.  340.  Describe  the  sim- 
ple pendulum.  341.  What  are  the  four  laws  of  the  pen- 
dulum ?  342.  Establish  each  of  these  laws.  343.  What  is 
the  formula  of  the  pendulum  ?  344.  Describe  the  compound 
pendulum.  345.  Show  that  the  centres  of  oscillation  and  sus- 
pension are  interchangeable  ?  346.  Explain  the  use  of  the 
pendulum  in  measuring  the  force  of  gravity.  347.  Show  that 
the  intensity  of  gravity  varies  directly  as  the  mass  of  the  body 
acted  upon.  348.  Show  that  the  moon's  path  is  curved  by 
gravity.  349.  Show  that  the  paths  of  the  planets  are  curved 
by  gravity.  350.  Show  that  the  paths  of  their  moons  are 
curved  by  gravity.  351.  Illustrate  and  explain  the  resolution 
of  forces.  352.  Explain  how  it  is  that  the  planets  can  recede 
from  the  sun  after  they  have  approached  him.  353.  Show 
that  the  force  which  causes  a  planet  to  describe  an  ellipse  must 
vary  inversely  as  the  square  of  the  distance  of  the  body  from 
the  sun.  354.  In  what  kind  of  orbits  do  the  comets  move? 
355.  Show  that  the  form  of  these  orbits  is  the  result  of  the 
action  of  gravity.  356.  Explain  the  perturbation  called  the 
moon's  variation.  357.  Explain  the  mutual  perturbations  of  Ju- 
piter and  Saturn  due  to  the  inequality  of  long  period.  358.  Ex- 
plain how  the  amount  of  the  perturbation  of  the  planets  can  be 
calculated.  359.  Do  the  observed  motions  of  the  planets  agree 
with  their  computed  disturbances  ?  360.  What  do  the  per- 
turbations of  the  moon  and  planets  prove?  361.  Show  that 
the  theory  of  gravitation  holds  good  throughout  the  uni- 
verse. 362.  Give  an  account  and  an  explanation  of  the  tides. 
363.  Account  for  the  spheroidal  form  of  the  earth.  364.  Ex- 
plain the  precession  of  the  equinoxes.  365.  What  do  the  tides, 
the  spheroidal  form  of  the  earth,  and  the  precession  of  the 
equinox  prove  ?  366.  Give  an  account  of  the  Schehallien  ex- 
periment, and  show  how  the  weight  of  the  earth  was  deter- 
mined by  it.  367.  Give  an  account  of  the  Cavendish  experi- 
ment, and  show  how  the  weight  of  the  earth  was  found  by  it. 
368.  Give  an  account  of  the  Harton  Coal  Pit  experiment, 
and  show  how  the  weight  of  the  earth  was  determined  by 
it.  369.  Explain  how  the  weight  of  the  sun  can  be  found? 
370.  Explain  how  a  planet  attended  by  a  moon  can  be  weighed  ? 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.  353 

371.  How  can  a  planet  not  attended  by  a  moon  be  weighed  ? 

372.  Explain  how  the  weight  of  the  moon  can  be  found  from 
the  tides.     373.     Explain  how  the  weight  of  the  moon  can  be 
found  by  means  of  the  apparent  displacement  of  the  sun  caused 
by  the  action  of  the  moon  upon  the  earth.     374.     About  what 
do  all  the  systems  of  the  heavenly  bodies  revolve  ? 

CONSERVATION   OF   ENERGY. 

375.     Define    and  illustrate    actual  and    potential  energy. 

376.  Define    mechanical,   molecular,    and    muscular    energy. 

377.  What  are  the  forces  that  tend  to  convert  potential  into 
actual  energy  ?      378.      Show  that  each  of  these  forces  tends 
to  do  this.     379.     Show  that  mechanical  energy  may  be  con- 
verted  into    heat.     380.     Describe    Count   Rumford's   experi- 
ment.     381.      Describe    Sir    Humphrey    Davy's   experiment. 
382.     What  do  these  experiments  show?     383.     Into  what  is 
all    mechanical    energy    ultimately    converted  ?      Show   this. 
384.     What  is  the  mechanical  equivalent  of  heat  ?     385.     Show 
how  this  equivalent  is  found.     386.      Into  what  may  heat  be 
converted  ?     387.     Illustrate  this.     388.     Show  that  the  same 
amount  of  heat,  when  converted  into  mechanical  energy,  always 
gives  rise  to  the  same  amount  of  energy.     389.     To  what  does 
the  energy  of  affinity  always  give  rise  ?     390.     Find  how  many 
foot-pounds  of  energy  are  developed  by  the  burning  of  a  pound 
of  hydrogen.     391.     Of  a  pound  of  carbon.     392.     Show  that 
the  energy  of   affinity  sometimes  appears  as  muscular  force. 
393.     Can  energy  be  destroyed  ?    394.     What  is  the  source  of 
all  the  energy  that  appears  on   the  earth  ?     395.     Show  that 
this  is  so.     396.     What  is  the  amount  of  heat  given  out  by  the 
sun  ?     397.     How  can  it  be  found  ?     398.    .Why  does  it  seem 
that  the  sun's  heat  cannot  be  developed  by  ordinary  combus- 
tion ?     399.     Give  an  account  of  the  meteoric  theory  of  solar 
heat.    400.     Of  the  nebular  hypothesis.     401.     Of  Helmholtz's 
theory  of  solar  heat.     402.     What  is  the  relation  between  the 
theories  of  Mayer  and  Helmholtz  ? 


w 


INDEX. 


£3T  For  concise  statements  of  the  leading  topics  of  the  book,  see  the  SUMMARIES, 
which  will  be  readily  found  by  means  of  the  Table  of  Contents.  The  references  in 
this  Index  are  only  to  the  fuller  treatment  of  subjects  in  the  body  of  the  work. 


A. 

Aberration  of  light,  80. 
Adams,  and  the  discovery  of  Neptune,  178. 
Aldebaran,  188.  327. 
Algenib,  26. 

Algol,  a  variable  star,  188,  326. 
Alpha  Centauri,  parallax  of,  81. 
period  of,  94. 
rate  of  motion  of,  96. 
Alphabet,  the  Greek,  323. 
Altitude,  20. 
Andromeda,  326,  335. 

nebula  in,  83. 
Angle,  sine  of,  303. 

supplement  of,  304. 
Antares,  188,  325,  330. 
Aphelion,  42. 
Apogee,  33,  131. 
Apsides,  33. 

Aquarius,  or  the  Water-bearer,  326,  337. 
Aquila,  or  the  Eagle,  325,  336. 
Ara,  or  the  Altar,  334. 
Aratus,  333. 
Arcturus,  color  of,  1 88. 

distance  of,  83. 

proper  motion  of,  90. 

rate  of  motion  of,  96. 
Argo  Navis,  or  the  Ship  Argo,  333,  340. 
Aries,  or  the  Ram,  327. 
Ascension,  right,  26. 
Asteroids,  165  (see  Minor  Planets). 
Astrasa,  discovery  of,  165. 
Atoms,  270. 

Atwood's  machine,  204. 
Auriga,  or  the  Charioteer,  327. 
Axis,  celestial,  8. 

of  earth  points  always  in  the  same 
direction,  77. 

B. 

Base  line  measured,  59. 
Bear,  the  Great,  5,  323,  334. 
Beehive,  the  (see  Praesepe). 
Bode's  Law,  161,  179. 
Bootes,  324,  335. 


Calendar,  the,  307. 

the  Gregorian,  307. 
Cancer,  or  the  Crab,  329. 


Canes  Venatici,  or  the  Hunting  Dogs, 

326,  330,  334. 

Canis  Major,  or  the  Great  Dog,  329,  339. 
Minor,  or  the  Little  Dog,  329,  339. 
Capella,  change  in  brightness  of,  189. 
color  of,  1 88. 
rate  of  motion  of,  96. 
Capricornus,  or  the  Goat,  326,  338. 
Cassiopeia,  5,  190,  324,  335. 
Cavendish  experiment,  251. 
Celestial  axis,  8. 

poles,  8,  213,  276. 
Centaurus,  or  the  Centaur,  333. 

cluster  of  stars  in,  194. 
Centrifugal  force,  or  tendency,  241. 
Cepheus,  324,  335. 
Ceres,  discovery  of,  162. 
Cetus,  or  the  Whale,  328,  338. 
Changes  of  seasons,  24.  , 

Coal-Sack,  the,  192. 
Coma  Berenices,  or  Berenice's  Hair,  330, 

334- 

Comet,  Biela's,  183. 
Donati's,  184. 
Encke's,  183. 
Halley's,  183. 
Comets,  181. 

parabolic  motion  of,  225. 
of  1680,  1811,  1843,  and  1861,  184. 
Conjunction,  22,  33,  46. 

inferior  and  superior,  45. 
Constellations,  186,  323. 

zodiacal,  187,  333. 

Co-ordinates  of  a  heavenly  body,  13. 
Copernicus,  a  lunar  mountain,  123. 

system  of,  39. 
Cor  Caroli,  325. 
Corona.Australis,  or  the  Southern  Crown, 

334- 
Corona  Boreafis,  or  the  Northern  Crown, 

325.  336. 

Corona  in  solar  eclipse,  112. 
Corvus,  or  the  Crow,  330. 
Crater,  or  the  Cup,  333. 
Cycles  and  epicycles,  37. 
Cygnj,  61,  parallax  of,  82. 
period  of,  94. 
proper  motion  of,  90. 
rate  of  motion  of,  96. 
Cygnus,  or  the  Swan,  325,  337. 


Day,  length  of,  24. 
lunar,  33. 


356 


INDEX. 


Day,  sidereal,  17. 

solar,  21. 
Declination,  26. 

Delphinus,  or  the  Dolphin,  327. 
Denebola,  26,  329. 
Distance  of  planets  from  sun,  49. 
of  sun,  23. 
polar,  13. 

Dominical  letter,  the,  308. 
Draco,  or  the  Dragon,  324,  336. 


Earth,  the,  129. 

a  molten  mass,  240. 
asrseen  from  the  moon,  132. 
heV  density  as  found  by  Cav- 
endish experiment,  254. 
her  density  as  found  by  Har- 
ton   Coal   Pit   experiment, 
257- 
.her  density  as  found  by  Sche- 

hallien  experiment,  250. 
her  distance  from 'sun,  53. 
path  curved  by  gravity, -218. 
periodic  time  of,  45. 
rotation    proved    by    experi- 
ment, 10. 

.  :   semi-diameter  found,  57. 
spheroidal  form  of,  65,  240. 
unvarying  direction  of  axis  of, 

77- 

weight  of,  247. 
Eclipses,  cycle  of,  150. 

may  occur  when,  143. 
of  moon,  142,  148. 
"       "      used  to  find  her  dis- 
tance, 67. 
of  sun,  145. 
Ecliptic,  the,  23,  29. 
Ellipse,  construction  of,  41. 
Ellipses  of  the  planetary  orbits  caused  by 

gravity,  2-21. 
Energy,  actual,  273. 

mechanical,  273. 

converted  into  heat, 

275,  278. 
molecular,  274. 

"         converted  into  heat, 

*...'•'  283. 
"         converted    into  elec- 

'tricity,  284. 
muscular,  274,  286. 
of  •affinity,  274,  284,  286. 
"  cohesion,  274,  283. 
"gravity, '2 74,  291. 
potential,  273. 
source  of,  287. 

transmuted,  not  destroyed,  286. 
Epact,  312. 
Epicycles,  37. 

Epicycloid,  the  moon's  orbit  an,  134. 
Equator,  ce'estial,  26,  44. 
Equatorial,  the,  6. 
Equinoxes,  26. 

precession  of,  27,  78,  242. 
Equuleus,  or  the  Little  Horse,  333. 
Eratosthenes,  a  lunar  mountain,  140. 


Eridanus,  or  the  River  Po,  333. 
Eudoxus,  333. 

F. 

Faculas,  solar,  no. 
Force,  centrifugal,  241. 

curving  the  planetary  orbits,  207. 
Forces,  atomic,  270. 

resolution  of,  221. 
Foucault's  experiment,  12. 


G. 


Galaxy,  the  (set  Milky  WayX 
Gemini,  or  the  Twins,  328,  339. 
Golden  number,  310. 
Gravity,  202,  274. 

causes  all  bodies  to  fall  at  same 
rate,  209.    • 

causes  bodies  to  fall  16  feet  a 
second,  215. 

curves  the  moon's  path,  216. 

varies  as  the  mass  of  bodies,  216. 


II. 


Harton  Coal  Pit  experiment,  210. 

Harvest  moon,  134. 

Heat,  converted  into  mechanical  energy, 

280. 
Count  Rumford's  experiments  on, 

275- 

Davy  s  experiments  on,  277. 
from  affinity,  284. 
"     mechanical  energy,  273,  278. 
"     molecular         "        283. 
mechanical  equivalent  of,  280. 
amount  of  solar,  289. 
Helmholtz's  theory  of  solar,  295. 
meteoric  '      291. 

unit  of,  280. 
Heavens,  a  dial,  151. 
Hercules,  325,  336. 

cluster  of  stars  in,  194. 
motion    of   solar    system    to- 
wards, 91. 
Horizon,  30,  306. 
Hyades,  the,  327. 
Hydra,  329,  340. 


Inequality  of  long  period,  229. 

J. 

Juno,  discovery  of,  164 
Jupiter,  apparent  motion  of,  35. 

distance,  period,  size,  etc.  of,  167. 

moons  of,  170,  233,  322. 

path  curved  by  gravity,  218. 

perturbations  of,  229. 

physical  features  of,  168. 


INDEX. 


357 


K. 

Kepler,  a  lunar  mountain,  139. 
laws  of,  41. 
system  of,  40. 


Law,  Bode's,  161,  179. 
Laws,  Kepler's,  41. 

of  motion,  201. 

of  pendulum,  211. 
Leo,  or  the  Lion,  329,  340. 
Lepus,  or  the  Hare,  328,  339. 
Le  Verrier,  and  the  discovery  of  Nep- 
tune, 154. 

Libra,  or  the  Balance,  330,  340. 
Libration  of  moon,  130. 
Light,  aberration  of,  80. 

interference  of,  185. 

velocity  of,  83. 

zodiacal,  127. 

Linne,  a  lunar  crater,  140,  317. 
Lunar  day,  33. 

month,  32. 

Lupus,  or  the  Wolf,  334. 
Lyra,  or  the  Lyre,  324,  336. 
Lyrae  Epsilon,  91. 


M. 

Machine,  Atwood's,  204. 
Magellanic  clouds,  196. 
Mars,  37,  157- 

his  distance,  size,  etc.,  157. 

from  sun  found,  51, 
physical  features  of,  158. 
mass  of,  258. 
Mercury,  37,  45,  120. 

apparent  motion  of,  34. 
atihosphere  of,  124. 
distance,  size,  etc.  of,  120. 
mass  of,  259. 
•'    phases  of,  121. 
rotation  of,  122. 
seasons  of,  123. 

Meridian,  measurement  of,  57. 
Meteoric  rings,  1 56;  • 
showers,  154. 
stones,  157. 
Meteors,  154. 
Metre,  French,  313. 
Metric  system,  312. 
Milky  Way-,  191. 

distance  of  stars  in,  83. 
Mira,  a  variable  star,  189,  328. 
Month,  lunar,  32. 
Moon,  apparent  motion  of,  32.     ' 
apparent  size  of,  1 18. 
atmosphere  of,  141. 
Moon, 

cycle  of,  280. . 
distance  of,  129. 

"  .      found,  61. 
disturbed  by  Venus,  234. 
eclipses  of,  142,  148. 


Moon,  harvest.  134. 

her  effect  in  precession,  246. 
libration  of,  139. 
mass  of,  260. 
of  Neptune,  178,  322. 
orbit  of,  33. 
-  parallax  of,  71. 
path  curved  by  gravity,  216. 
period  of,  130, 
perturbations  of,  226. 
phases  of,  130. 
rotation  of,  131. 
shadow  of,  142. 
size  of,  129. 
surface  of,  135. 
tides  caused  by,  237. 
variation  of,  227. 
Moons,  89. 

of  Jupiter,  170,  322. 
"  Saturn,  173,  322. 
,      "  Uranus,  177,  322. 
Motion,  curvilinear,  206. 
elliptical,  221. 
laws  of,  201. 
parabolic,  225. 
Mural  circle,  18. 


<    ."-•  N. 

Nebula,  crab,  86. 

dumb-bell,  86. 
in  Andromeda,  83. 
ring,  86. 

Nebular  hypothesis,  the,  294. 
Nebulae,  83,  193. 

distance  of,  87. 
number  and  nature  of,  86,  88. 
variable,  195. 
Neptune,  discovery  of,  178. 

distance,  size,  etc.  of,  178. 
Nodes,  33,  75. 
Nubeculae,  196. 
Nutation,  79. 


O. 


Occultation  of  stars  by  moon,  142,  150. 
Olbers  on  the  origin  of  the  minor  plan- 
ets,. 164. 

Opposition,  33,  46. 
Ophiuchus,  or  the   Serpent-bearer,  325, 

Orbits   of  planets  inclined  to  plane   of 

ecliptic,  75. 

Orion,  328,  338.  . 

Orionis,  Theta,  93. 


P. 

Pallas,  discovery  of,  165. 
Parabolic  motion  of  comets,  225. 
Parallax,  68. 

of  the  fixed  stars,  72,  73. 

"     "   moon,  71. 
Pegasus,  or  the  Winged  Horse,  326,  335. 


358 


INDEX. 


Pendulum,  the,  12,  201,  210,  252,  255. 
compound,  213. 
formula  of,  213. 
laws  of,  211,  212. 
reversible,  214. 
simple,  211. 

used  to  measure  force  of  grav- 
ity, 214. 

Perigee,  33,  131. 
Perihelion,  41. 
Period,  sidereal,  46,  47. 

synodic,  46. 
Perseus,  326,  335. 

cluster  of  stars  in,  194. 
variable  star  in  (see  Algol). 
Perturbations  of  the  moon,  226. 

moons  of  Jupiter,  233. 
planets,  229. 

"        how  comput- 
ed, 232. 

Pisces,  or  the  Fishes,  327. 
Piscis  Australis,  or  the  Southern  Fish, 

326. 

Planets,  apparent  motions  of,  34. 
curved  orbits  of,  207. 
inclination  of  the  orbits  of,  75. 
inferior  and  superior,  46. 
inner  group  of,  160. 
mean  distances  from  sun,  65. 
minor,  161,  319. 

move  in  ellipses  because  of  grav- 
ity, 221. 

orbits  curved  by  gravity,  220. 
perturbations  of,  229. 
relative  distances  from  sun,  53. 
secular  perturbations  of,  236. 
synodic  periods  of,  45. 
Pleiades,  a  cluster  in  Taurus,  193,  327, 

338. 

Poles,  celestial,  8,  213,  276. 
Praesepe,  a  cluster  in  Cancer,  193,  329. 
Ptolemaic  system,  35. 


R. 

Refraction,  8,  73. 

in  lunar  eclipse,  149. 
Resolution  of  forces,  221. 
Retrograde  motion  defined,  177. 
Right  ascension,  26. 


S. 


Sagitta,  or  the  Arrow,  327. 
Sagittarius,  or  the  Archer,  325,  337. 
Scorpio,  or  the  Scorpion,  325,  330,  337. 
Serp'ens,  or  the  Serpent,  325. 
Satellites  89  ( see  Moons). 
Saturn,  distance,  period,  size,  etc.  of,  172. 

moons  of,  173,  322. 

perturbations  of,  229. 

rings  of,  173. 

Schehallien  experiment,  247. 
Seasons,  the,  25. 
Sector,  zenith,  58,  248. 
Secular  changes,  236. 
Shadow  of  the  earth,  3,  142. 


Shadow  of  the  moon,  142. 
Shape  of  the  earth,  3. 

"       sun,  moon,  and  planets,  4. 
Sine  of  angle  defined,  303. 
Sirius,  329. 

color  of,  1 88. 
distance  of,  83. 
name  of,  187. 
proper  motion  of,  90. 
rate  of  motion  of,  96. 
Solar  system,  motion  of,  90. 

position  of,  192. 
Solstices,  27. 
Star,  Polar,  5,  16,  324. 
Stars,  apparent  motions  of,  5. 
circumpolar,  5,  323. 
clusters  of,  193. 
color  of,  187. 
double,  91. 

periods  of,  94. 
physical  and  optical,  92. 
revolve   about  common  centre  of 

gravity,  262. 
fixed,  185. 

'      distance  of,  76. 
"     proper  motion  of,  90,  95. 
magnitudes  of,  186. 
names  of,  187. 
nebulous,  195. 
number  of,  185. 
of  first  magnitude,  332. 
temporary,  190. 
twinkling  of,  185. 
variable,  188. 
Style,  old  and  new,  307. 
Sun,  apparent  diameter  of,  27. 

path  of,  28. 

appearances  in  total  eclipse  of,  in. 
as  a  fixed  star,  95. 
axial  rotation  of,  103. 
distance  of,  51. 
eclipses  of,  145. 
Hind's  description  of  total  eclipse 

of,  147- 

planetary  orbits  curved  towards,  207. 
"pores,"   "willow  leaves,"  etc.  on 

the,  no. 

position  of  axis  of,  104. 
revolves  round  centre  of  gravity  of 

solar  system,  262. 
size  of,  99. 
spots,  101. 

'      appearances  of,  105. 
"      changes  of,  108. 
1      dimensions  of,  107. 
"      motion  of,  102,  105. 
"      nature  of,  113. 
weight  of,  257. 
System,  metric,  282. 

of  Copernicus,  39. 

"  Kepler,  40. 

"  Ptolemy,  35. 

"  Tycho  de  Brahe,  40. 

T. 

Taurus,  or  the  Bull,  327,  338. 
Theodolite,  63. 


INDEX. 


359 


Tides,  237. 

neap,  239. 

spring,  239. 

weight  of  moon  found  from,  259. 
Transit  instrument,  15. 
Transits  of  Venus,  54,  65,  76,  126. 
Trial  and  error,  method  of,  40,  72. 
Triangle,  right,  303. 

oblique,  303. 

computation  of  parts  of,  304. 
Triangulation,  59. 
Triangulum,  or  the  Triangle,  327. 
Twilight,  29. 

duration  of,  30. 
Tycho,  a  lunar  mountain,  136. 


U. 


Universe,  gravity  acts  throughout  the,  234. 
Uranus,  discovery  of,  176. 

distance,  period,  size,  etc.  of,  177. 

moons  of,  177,  322. 

perturbations  of,  178. 
Ursa  Major,  or  the  Great  Bear,  323,  334. 
Minor,  or  the  Little  Bear,  324,  334. 
Ursae  Majoris,  Xi,  93. 


V. 
Vega,  6,  324. 

parallax  of,  82. 
rate  of  motion  of,  96. 
Venus,  36,  38,  45,  124. 

apparent  motion  of,  34. 

atmosphere  of,  126. 

distance  from  sun,  124. 

disturbs  our  moon,  234. 

her  distance  from  sun  found,  49. 


Venus,  mass  of,  258. 

period  of  revolution  and  rotation, 
125. 

seasons  of,  126. 

size  of,  124. 

transits  of,  54,  65,  76,  126. 
Vesta,  discovery  of,  164. 
Via  Lactea  (see  Milky  Way). 
Virgo,  or  the  Virgin,  330,  337,  340. 
Volcanoes,  lunar,  135,  140. 

W. 

Weight  of  earth,  257. 

"  moon,  259. 

"  planets,  258. 

"  sun,  257. 
Weights,  metric  system  of,  282. 


Y. 

Year,  civil,  307. 
Julian,  307. 
leap,  308. 
sidereal,  22,  27. 
tropical,  27,  308. 


Z. 

Zenith  sector,  58,  248. 
Zodiac  defined,  187. 

constellations  of,  187,  333. 

signs  of,  187. 
Zodiacal  light,  127. 
Zone,  torrid,  24. 
Zones,  frigid,  24. 

.  temperate,  25. 


THE   END. 


Cambridge  :  Electrotyped  and  Printed  by  Welch,  Bigelow,  &  Co. 


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